There is a rule if it is in the form of sqrt(sqrt(x+y)-2sqrt(x.y)) then the result is sqrt(x)-sqrt(y). For this question sqrt(sqrt(2+1)-2[sqrt(2)*sqrt(1)])=sqrt(2)-sqrt(1)=sqrt(2)-1
Well it's better to be said identity, since it holds for all Reals. Like a process has a rule to (for example) integrate by parts, you assume 1 function to be 1st and other to be second then you apply the formula of rule. Just my take.
This doesn't look exactly right. Square your RHS. You get (x + y) - 2 sqrt(xy). You need to lose one "sqrt" on the left hand side. To wit: sqrt((x + y) - 2 sqrt(xy)) = +/- (sqrt(x) - sqrt(y)), with the sign chosen on the RHS to ensure the number is positive.
China and Romania have always been at the top when in comes to math, but I don't necessarily think the method used to achieve that goal was a positive one.
Sadly I was totally confused. She showed us a rather lengthy process, but with ABSOLUTELY NO explanation for why we are doing all these arcane steps. I think this is probably the worst possible explanation of how to achieve the objective, because she showed us WHAT to do but with no explanation at all of WHY.
I would say that's not her fault but more the fault of mathematics. There is no rule or formula to ever tell you what to do next. In mathematics the only good answer to why did you do this is "because it works"
Sometimes I ask my self what is the benefit of such math, it is like guessing not a direct math , useless in normal job life , don’t expect nowadays mobile / comp. generation children need such bla bla
@@somgesomgedus9313 Actually I must respectfully disagree. To suggest that "because it works" is the only explanation needed in maths encourages rote learning, instead of gaining a true understanding of what you are doing, and why. Mathematics is a language used for the manipulation of symbols: "because it works" is like learning the words of a spoken language without learning their meaning. It renders you helpless when faced with a novel situation, and that is not how we should teach maths.
Instead of looking for (a-b)^2 = 3 - 2 sqrt(2), I looked for (a + b sqrt(2))^2 = (3 - 2 sqrt(2)), with a, b rational numbers. The advantage here is that I don't have to pull a and b out of thin air: I can solve for them. In this case we have a^2 + 2 b^2 = 3 and 2ab = -2. There are two solutions here: a = -1, b = 1, and a = 1, b = -1. The latter choice is the positive result implied by the radical. So the answer is -1 + sqrt(2). How did I know to look for an answer in this form? From more advanced math, I know that Q[sqrt(2)] is a field, which means specifically for us that it's closed under multiplication. So it's a good place to start when looking for roots of a polynomial.
You can also use the fact that for a = sqrt(3 - sqrt(8)) and b = sqrt(3 + sqrt(8)) we find that ab = 1 and a + b = sqrt(8), hence x^2 - sqrt(8)x + 1 = 0 have - 1 + sqrt(2) and 1 + sqrt(2) for solution.
When I went to a secondary modern senior school in 1958 I was taught to be literate and numerate, I worked as a precision engineer but I don't have a clue what the lady is talking about.
I know the trick too.... But if anybody don't know the trick of solving it directly....they too have to give a minute..... Professor of college who are doing PhD in mathematics don't know such trick and they may take a minute to solve it's doesn't mean that they know less math than you okay...... I hope you otherstand the difference
@@mathematicsman7454 I am not judging anyone as If someone is able to solve this problem she may be genius and the one who isn't is weak in maths . I was just saying that even in Maths Olympiad , there comes questions which can be solved just by basics ! Well I respect your opinion ..
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People saying this is too simple, and while it kind of is simple, it is also hard to come up with unless you are trained to apply this kind of thinking in problems. I would have never guessed to use the square of difference identity, feels like its a problem you have to be familiar with beforehand
It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡
"it is also hard to come up with unless you are trained to apply this kind of thinking in problems" . those who are spesicically trained for olympiands, will be trained for this and much more , becomes it too easy for them.
People commenting it is too simple are unrecognized genius. I wonder why they are wasting their time watching youtube videos. I mean, it is not the hardest question, but it does takes more thinking than a regular polynomial question and corresponds to high school students level
Appreciate that there are some Maths Olympiad questions within our grasp. I forgot the sqrt(square) trick from high school, but would have been able to do it then. These are like IIT JEE questions, maybe training questions, those students would argue. I expect IIT JEE students (even students) to call this easy by IIT JEE standard. Which would make me average in Maths. At 90 percentile in Quantitative Ability in the Stamford-Binet V test.
To simple 🙃 √( √9 - √8) √( 3 - √8) √( 3 - 2×1.41) √( 3 - 2.82) √( .18 ) => near to √16 So as my own formula 😂 ( work only when number are near to root ) Information √.16=> .4 √.18 .4 + 1/18 => .4 + .056 => .456 (it is approx without so much calculations 😅) Well the 1/18 , its come from my formula Like if someone root value are near to square √24 = √25 - (25-24)/( *2* * 25) *2* is constant 😊
You forgot that the square root of 9 is also minus 3, etc., square root of 8 has a plus and minus value as well, and the square root of a negative number will have an imaginary component. At the end you put in "absolute" sign for positive/real SOLUTION, but the absolute sign should have been used--three times , no?--in the question. NOW it's a math olympiad problem.
Correct. We usually restrict the solution to the positive square roots. However, the problem statement didn't limit it in that way, so all of the other roots apply - eight in total.
@@antronx7 I understand what you are trying to say but its a rule of mathematics that in Real numbers, √x is always non negative. What you mean to say is- Roots of X² are ±√(x²) See, the ± comes before a square root thing. This is because a square root can never be negative. In your case, X² = 9 X = ±√9 X = +3, -3
@@killanxv If (1) the coefficient in front of the second term is 2, and (2) the numbers summing to the first term are the same as factors multiplying to the radicand in the second term, then the answer is the sum or difference of the roots of the two numbers summing to the first term. See my post above. Gotta have that coefficient of 2 in front of the radical sign in the second term. √(15 + √200)) √200 = √(4 x 50) = 2√50. Bingo! Got the coefficient of 2. Now 10 + 5 = 15 and 10 x 5 = 50. Throw radical signs over 10 and 5 for your answer: √10 + √5. Note that we keep the sign in the original problem. Hope this helps.
Well we are not going to find it until we get fair question remember differential problem in 2021? İ dont know if youre university preparing student or you did but just check it out
do you all Know that math olympics have some simple questions here and there to slow participants down and reward faster solutions right? This Its ONE example of such questions. You solve it quickly to have more time to solve the actual problems Good luck with the other questions "genius"
It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡
@@eliasbram3710math olympiad problems usually have a trick to them that isn’t commonly known, that’s why they are so hard. this however, is a textbook example of denesting square roots most people interested enough in contest math algebra would know. unfortunately, it is clickbait. this is not a MO level problem
In1990ies in ist. muhendislik one of our friend proved a wellkown physics equation's incorrectnessby maths but these kids are smiling on you ,dont worry you're in the right path...
I like maths...but I absolutely hate when they get "creative" (i.e.: the only way to resolve a problem, instead of using a well stablished and proven algorithm, is having a happy idea). Thank God for calculus.
This method is called compleating the square. You map your current problem on the binomial formula and then use it to simplify the problem. Which she did. I did not watch the video with sound on. Not sure why everyone is so negative in the comments...
It's simple school book question in india probably from 8 or 9th grade it's just basic...😂 I didn't expect anything form American but atleast European can do it🤡😂...I guess now a days they are busy in teaching children about gender equality and lgbt😂🤡
Now √(√9 - √8) = √(3 - 2√2). Now suppose √(√3 - 2√2) = a + b√2, where a and b are integers. This maybe not actually have a solution in integers, but if it does, we can find them as follows. Let 3 - 2√2 = (a + b√2)² = (a² + 2b²) + 2ab√2 So, 3 = a² + 2b² and -2 = 2ab So, (a = 1 and b = -1) or (a = -1 and b = 1). However, a + b√2 ≥ 0, as otherwise √(√9 - √8) would be a complex number, so we are forced to conclude that a = -1 and b = 1 is the only possible solution. So, √(√9 - √8) = -1 + 1*√2 = √2 - 1.
I'd start by relaxing to let a, b be rational numbers. Then be pleasantly surprised when they turn out to be integers. The rest of the process is exactly the same.
I can do it shortly as to remove the whole square root and give power on both and cancel the square in to second rood know we get 9-8 and ans would be 1
I do not know how much time it would take for me until realizing that 3 - 2sqrt(2) can be easily presented in a form of a^2 - 2ab + b^2. Do mathematicians have a special ability to glance it on the spot when something can be recombined according to the known rule?
I think it is more about having experience and mastery with those tools. In many schools we skip to differentials and integrals before having a solid grasp on foundations of math. It's like they think mathematics was an intellectual desert up until newton and Leibniz. If students are educated to maximize their mathematical tools before learning new ones, they'd know how to solve these problems. (The Israeli school system is worse than the american, we don't even learn completing the square, so we'd have no intuition for solving this kind of problem)
@@TheMeiravital Thank God they did do that otherwise I would have failed math. Memorizing patterns is not as useful as understanding why. ESPECIALLY once you realize that in the real world math never works out nicely like that.
I thought I was the only one who had this shitty problem, I had to solve advanced math problems without having enough time to fully memorize algebra formulas due to lockdown. And now everyone is kicking ass
I think they just saw the same or very similar solutions over and over. I asked my math professor a question before and he solved it by adding 1 to the both sides of the equation. When I asked why would he do something weird like that and he told me that they just get used to this patterns over the years.
Esatto. Dai che a novembre quando non sarò più quello dei numeri e tiferò Putin che farà un bel botto nucleare vi regalerò giubbotti di plastica a specchio, piscine in muratura e motomacchine che sfrecciano a 500 orari. Da novembre ci divertiamo tutti contro tutti col finale nucleare planetario
I always see Indians in comment section only to brag about themselves. Usually this means a lack of confidence and self-respect. Is India one of the leaders in technology in the world?
Funny i always thought algebra was magical until i learned trigonometry. Then i was amazed on how it is used in daily life. I always questioned when i would need to use algebra in daily tasks... 😅
To solve the given expression, we can simplify it step by step: Simplify the square root of 9: v9=3 Simplify the square root of 8: v8=2v2 Substitute the simplified values back into the original expression: v3-2v2 Therefore, the solution to the given expression is v3-2v2
do you Know that math olympics have some simple questions here and there to slow participants down and reward faster solutions right? This Its one example of such questions. You solve it quickly to have more time to solve the actual problems
In everyday life no, but the general take away from problems like this is exercising the notion of manipulating mathematical expressions into different forms to make them simpler (i.e., easier to manage, interpret, etc). This particular example isn't that complicated, but the general skill of simplification can come in handy in certain jobs. Like if one were to come up with a certain formula to describe a particular phenomena that's unique to that company, someone else may want to manipulate the form of that formula so to make its terms more explicit.
To solve the problem here, two symbols used ie. "Is equal to" and "implies". For simplification "is equal to" is used. But to solve an equation "implies" symble is used.
Solved it in my head in less than 3 seconds, and I am 81. Of course I learned math before they “improved it.” And the instructor is wrong. The answer is 1.
Instead of doing this simply let the whole thing be x and form a quadritic equation and just solve it. Isn't it better to give all the possible values rather than just 1 value?
I have a backlog in math, so not a qualified person to address this, but any question is hard if you don't know the method to solve it. You know this already, sweetheart...❤
This is not a trick, come on, there is a principle behind it, no doubt, but you missed explaining it. It's a plai Deux Ex Machina going from the radical to the general formula of a 2nd degree polynom
Very amateur solution. This women is not a professional mathematician! (1) Some notation issues: The logic IMPLICATION symbol cannot substitute the equality symbol!!! The dot at the bottom cannot be used in a confusing way: if we want to represent multiplication, the dot should appear little higher , in the middle of the height of small letters . It can not be used in the same way as the decimal point (2) WHY her method works? There is not any commentary regarding the resolvability of the problem. Her method to simplify nested square root expressions [sqrt ( sqrt (a) - sqrt(b) ) ] is only working iff a-b is a PERFECT square. First this statement should be proven. After what we can attack the problem. (3) The women is not aware of the difficulty of real maths competition problems, if she is considering this one as an olympiad challenge.....A computation is only a computation. Nothing else!