Question

Find positive integer values of a and b given that:
(5+√a)^2 = b+20√7
​

Answer 1

a = 7, b = 32

Explanation:

Expand (5 +
`√(a)`)²

noting that
`√(a)` ×
`√(a)` = a

Hence

(5 +
`√(a)`)² = 25 + 10
`√(a)` + a

Compare the values to b + 20
`√(7)`

For the 2 sides to be equal then

`√(a)` =
`√(7)` ⇒ a = 7

and b = a + 25 = 7 + 25 = 32