Non-standard Exponential Equation! / How to solve in two ways?

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In this video we are going to solve an non-standard exponential equation.
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Опубликовано:

8 сен 2024

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Комментарии : 42

@user-tt4ep6fr4d 3 года назад

The quadratic formula The denominator is 2a but not 4a You forgot Please correct it

@intellecta2686 3 года назад

Yes, of course I will make another video just about it :) Nooot , but will pin you!

@holyshit922 3 года назад

@@intellecta2686 From Vieta we have x_{1}+x_{2}=-b/a Suppose that x_{1}-x_{2}=d (x_{1}-x_{2})^2 is symmetric function and it is called discriminant (x_{1}-x_{2})^2 is symmetric function so it can be expressed in terms of elementary symmetric functions (x_{1}-x_{2})^2=(x_{1}+x_{2})^2-4x_{1}x_{2} (x_{1}-x_{2})^2=(-b/a)^2-4(c/a) x_{1}+x_{2}=-b/a x_{1}-x_{2}=d 2x_{1}=-b/a+d 2x_{2}=-b/a-d d^2=(b^2-4ac)/a^2 so x_{1} = (-b+sqrt(b^2-4ac))/(2a) x_{2} = (-b+sqrt(b^2-4ac))/(2a) Symmetric functions can be also used for solving cubics and quarics

@mohamed29620 3 года назад

@@intellecta2686 thanks for the demonstration

@SALogics 3 месяца назад

Please use one method in a video and make another video for second method to keep the length of video short, Thanks a lot❤❤

@Anoxonamoon 3 года назад

it's (1+√5)/2 and x=log3/2((1+√5)/2)≈ 1.18 thank you for the video and btw i loved the posters

@intellecta2686 3 года назад

Yes, true! Thanks, I like them too:)

@johnwindisch1956 2 года назад

Identifying the quadratic equation for a solution seemed to be the most important part. Thanks Ivana and Simba(?)

@tusharsachdeva4781 2 года назад

If my teachers were like this, I would top my exams

@roger7341 10 месяцев назад

This is a popular Golden Ratio problem where Φ = (√5 + 1)/2 = (3/2)^x. To see this, divide the given equation by 6^x to obtain (3/2)^x - 1 = 1/(3/2)^x, which is Φ - 1 = 1/Φ or Φ^2 - Φ - 1 = 0 with the above claimed solution. Thus, x*ln(3/2) = lnΦ or x = lnΦ/ln(3/2) = 1.18681...

@Paul-222 Год назад

I used the Lambert W function to solve it.

@e-learningtutor1351 3 года назад

It's really interesting listening ur lecture.. Subscribed

@radupopescu9977 3 года назад

I have a problem (in fact I designed it) and I am struggling to solve it, other than by graphs. I am not a mathematician, I only play sometimes with math... when I am in the mood to... I try W Lambert and a lot of things but it didn't work. The equation is (4^x)/x + (4^(1/x))*x=12. The real solutions are 0.5 and 2 and many other complex solutions. I try to make substitutions and I get a/ln(a) + b/ln(b)=12/ln4, where a=4^x, and b=4^(1/x), and lna*lnb=(ln4)^2, but analytically I wasn't able to solve it... Maybe you have some suggestions?

@rmw6151 3 года назад

Thanks Ivana, a really interesting little problem requiring a bit of thought!

@intellecta2686 3 года назад

Thank you :)

@nasrullahhusnan2289 Год назад

In the second method you come up with d²=cd+c² It is indeed a quadratic equation in d, and you get one solution. But you forget that it is also a quadratic equation in c which will give you another solution.