Given equation is [tex]x^2 = a[/tex]
In general solution of [tex]x^2 = b[/tex] is [tex]x = + \sqrt{b} [/tex] and [tex]x = - \sqrt{b} [/tex]
So the solution of given equation is [tex]x = + \sqrt{a} [/tex] and [tex]x = - \sqrt{a} [/tex]
Now difference between them is 30.
So we can write
[tex] \sqrt{a} - (- \sqrt{a}) = 30 [/tex]
[tex] \sqrt{a} + \sqrt{a} = 30 [/tex]
[tex]2 \sqrt{a} = 30 [/tex]
[tex] \sqrt{a} = 15 [/tex]
On squaring both side
[tex]( \sqrt{a})^2 = (15)^2[/tex]
[tex]a = 225[/tex]
