- #1

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## Homework Statement

If x ε R, the numbers 5

^{1+x}+5

^{1-x}, a/2, 25

^{x}

+25

^{-x}form an AP, then 'a' must lie in the interval:-

a)[1,5)

b)[2,5]

c)[5,12]

d)[12,∞)

## Homework Equations

Not required

## The Attempt at a Solution

I substituted y=5

^{x}.

The terms are in AP, so the common difference is constant. That is:-

[tex]\frac{a}{2}-5y-\frac{5}{y}=y^2+\frac{1}{y^2}-\frac{a}{2}[/tex]

[tex]\Rightarrow a=y^2+\frac{1}{y^2}+5y+\frac{5}{y}[/tex]

Now i am stuck here. :(

Please somebody help.

Thanks!