KVPY SX SB Exam 2012 Question Paper

Question : 3 of 120

Marks: +1, -0

The maximum value M of

3^x+5^x-9^x+15^x-25^x

, as x varies over reals, satisfies

Solution:

M=a+b-a^2+ab-b^2

{a^2+b^2}/2 ≥ ab

a^2+b^2 ≥ 2ab

-(a^2+b^2) ≤ -2ab

M ≤ a+b-ab

m < 1-(a-1)(b-1)

min is zero
hence 0 < M < 2

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