The integral values of x for which `x^2 +17x+71` is perfect square of a rational number are a and b, then `|a-b|`=

Explanation

`x^2+17x+71=y^2`

`x^2+17x+71-y^2=0`

`x=(-17pmsqrt(289-4(71-y^2)))/2`

`=(-17pmsqrt(5+4y^2))/2`

x to be integer

`5+4y^2` is perfect square

`5+4y^2=k^2`

`k^2-4y^2=5`

...