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Who lied to you that 99% would fail and how can this question be an olympiads question when it is exyremely easy, I did it mentally without a pen, a piece of paper or calculator.
Before watching: This will go most easily if we square away the radicals on the left. Recall that a^(mn) = (a^m)^n. First, square the left and the right, to get 3sqrt(9 sqrt(27)) = 81^(6x) = 3^(24x) (because 3^4=81) Squaring again we get (3^2)(9)sqrt(27) = 81 sqrt(27)= 81^(12x) And with one last squaring... (81^2)(27) = 81^(24x). Since 81 = 3^4, 27 = 3^3, and (a^m)(a^n) = a^(m+n)... (3^4)^2 * 3^3 = (3^4)^(24x) -> 3^11 = 3^(96x). Then 11 = 96x, and finally x = 11/96
Rather than squaring expressions I converted them to exponential form right away: On the left 3^1/2 x 9^1/4 x 27^1/8, all powers of 3; on the right 3^12x. Add exponents on the left to get 11/8 with 12x on the right. X = 11/96.
I don't get it. Why not say 262144 - 1 ? If you are going to take the step that 512 is 2 to the ninth, why not say that 2 to the eighteenth is 262144 ?
This is super-stupid. If you know that 2^9 is 512, you could just do 512^2 - 1...factoring it into (512+1)(512-1) is the single dumbest way you could go about solving from there. But then you do a whole bunch of other time-wasting after.
@@proffessorclueless Just multiply 1024 x 256 -1. Simpler than all rearrangement. I know power of 2 up to 20 by heart (plus 2^24 and 2^32) as a low level computer guy.
ITNA LAMBA Q KIYA? 4^8/8^4 - 8^4/4^8 can also be written as 64*64*16/64*64 - 64*64/64*64*16 sare 64 cut jayenge, simple bachega 16 - 1/16 = (265-1)16 =255/16
The easiest solution is to put everything in powers of 2. You then have 2^2^8 / 2^3^4 - 2^3^4 / 2^2^8 = 2^16/2^12 - 2^12/2^16 = 2^4 - 1/2^4 = 16 - 1/16 = 255/16.
He wastes time on several steps. 3^x = 45 can immediately be re-written as log_3 (45) = x. We're not required to use log base 10 to eventually get to this step.
3²+3⁴=90, but answer is 9×5+9×5=45+45=90 because we have to so how much we can remember and show that why 3×3×3×3+×3×3 is 90 Which we never use in our life. I am not telling that math and science is useless be this this 💀😕 education system crush it and fuck it
If we divide by √x, we get 2=√x i.e. x=4. But the equation has one more solution (when division is invalid): x=0. (If x is negative, then √x is imaginary. More generally, if x is complex other than a positive real number, then angle of √x in polar coordinates can't be the same as the angle of x.) We can also substitute y=√x; then we get y^2 - 2*y = 0, and that yields y*(y-2)=0, immediately giving the two solutions (a quadratic equation can't have more than two solutions).
