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 = + √(b)` and
`x = - √(b)`

So the solution of given equation is
`x = + √(a)` and
`x = - √(a)`

Now difference between them is 30.
So we can write

`√(a) - (- √(a)) = 30`

`√(a) + √(a) = 30`

`2 √(a) = 30`

`√(a) = 15`

On squaring both side

`( √(a))^2 = (15)^2`

`a = 225`