Question

9^x+15^x=25^x please send me the answer​

Answer 1

Answer:

The maximum value M of 3x + 5x – 9x + 15x –25x , as x varies over reals, satisfies – (A) 3 < M < 5 (B) 0 < M < 2 (C) 9 < M < 25 (D) 5 < M < 9 Read more on Sarthaks.com - https://www.sarthaks.com/386136/the-maximum-value-m-of-3-x-5-x-9-x-15-x-25-x-as-x-varies-over-reals-satisfies

Answer 2

Let a=3xa=3x and b=5x,b=5x, Then expression convert into f(a,b)=a+b−a2+ab−b2f(a,b)=a+b−a2+ab−b2

So

f(a,b)=−12[2a2+2b2−2ab−2a−2b]f(a,b)=−12[2a2+2b2−2ab−2a−2b]

So

f(a,b)=−12[(a2−2a+1)+(b2−2b+1)+(a2+b2−2ab)−2]f(a,b)=−12[(a2−2a+1)+(b2−2b+1)+(a2+b2−2ab)−2]

So

f(a,b)=−12[(a−1)2+(b−1