Question

Prove that `(12)/(3 + sqrt5 - 2 sqrt2) = 1 + sqrt5 + sqrt10 - sqrt2`

Answer 1

`(3 + sqrt5 -2 sqrt2) (1 + sqrt5 + sqrt10 - sqrt2)`
`= 3 + sqrt5 - 2 sqrt2 + 3 sqrt5 + 5 -2 sqrt10 + 3 sqrt10 + 5sqrt2- 4sqrt5 - 3sqrt2 - sqrt10+4`
= 12
`:. 1 + sqrt5 + sqrt10 - sqrt2 = (12)/(3 + sqrt5 - 2 sqrt2)`
Hence, `(12)/(3 + sqrt5 -2 sqrt2) = 1 + sqrt5 + sqrt10 - sqrt2`