A awesome mathematics problem | Olympiad rational Question | can you solve this problem | x=?

#quantativeaptitude #maths #olympiad#rational#exponents #integral
france math olympiad question | can you solve this? | x=?, can you solve this math problem,can you solve this challenging problem?,can you solve this equation,can you solve this puzzle,learn how to solve this challenging problem,can you solve this maths puzzle,math olympiad algebra problem,how can solve this puzzle,math olympiad problem,olympiad mathematics,math olympiad problems,mathematics olympiad,mathematics

[raghvendrasingh]

Nice problem
a+b = 4 and a^5+b^5 = 2^10
now (a+b)^5 - a^5 - b^5 = 5 ab(a+b)(a^2+ab+b^2)
hence
4^5 - 2^10 = 5 ab (a+b) ( a^2
+ab+b^2)
20 ab ( 16 - ab ) = 0
now a > 0 hence either b = o or ab = 16
if b=0 then x= 2^18 = 262144
if ab = 16 then 16 = 2^10 - x
x = 1008

[michaeldoerr]

The answer is 2^18. I am in awe that there was a need ro apply techniques for Diophantine equations twice or thrice. I better that for practice!!!

[souzasilva]

Don't know how to write a radical correctly?

[raghvendrasingh]

correction in last comment 16^5 = 2^10 - x from which x < 0 not possible only solution is x = 262144