Question

The difference between the solutions to the equation x2 =a is 30 what is a ?

Answer 1

Given equation is $x^2 = a$

In general solution of $x^2 = b$ is $x = + \sqrt{b}$ and $x = - \sqrt{b}$

So the solution of given equation is $x = + \sqrt{a}$ and $x = - \sqrt{a}$

Now difference between them is 30.
So we can write
$\sqrt{a} - (- \sqrt{a}) = 30$
$\sqrt{a} + \sqrt{a} = 30$
$2 \sqrt{a} = 30$
$\sqrt{a} = 15$

On squaring both side
$( \sqrt{a})^2 = (15)^2$
$a = 225$