If the terms of G.P. `sqrt(a-x),sqrt(x),sqrt(a+x)`.. are all in integers where `agto` then the least composite odd integral value of `a` is

Options

A. `9`
B. `15`
C. `45`
D. `49`

Answer

C

Explanation

`2sqrt(x)=sqrt(a-x)+sqrt(a+x)`
`implies4x=2a+2sqrt(a^(2)-x^(2))`
`impliessqrt(a^(2)-x^(2))=2x-aimpliesa^(2)-x^(2)=(2x-a)^(2)`
`implies x=0` or `(4a)/5`
terms of the A.P. are `sqrt(a/5),2,sqrt(a/5),3sqrt(a/5)`,……… which are integers.
`impliesa=5n^(2),"n"epsilonN`
`:.` for `n=1,a=5rarr` which is not composite
for `n=2, a=20rarr` which is composite but not odd
for `n=3, a=45rarr` which is the least odd composite