If the terms of the A.P. `sqrt(a-x),sqrt(x),sqrt(a+x)` are all in integers, `w h e r ea ,x >0,` then find the least composite value of `adot`

Explanation

`sqrt(a-x),sqrtx,sqrt(a+x)` in A.P
`rArr2sqrtx=sqrt(a-x)+sqrt(a+x)`
`sqrt4x=a-x+a+x+2sqrt(a^(2)-x^(2))` (squaring both sides)
`rArr2x-a=sqrt(a^(2)-x^(2))`
`rArr4x^(2)-4ax+a^(2)=a^(2)-x^(2)`
`rArr5x^(2)=4ax`
`rArra=(5x)/4`
Now, x must be perfect square as `sqrtx` is an integer.
`rArr` x=1,4,9,16,...etc.
For x=1,a=`5/4` (rational number)
for x=4,a=5(prime number)
For x=9,a=`(45/4)` (rational number)
for x=16,a=20 ( composite number)
Hence, least composite value of a is 20.