DO NOT USE A CALCULATOR IN THIS QUESTION. Express ((4√(5)-2)^(2))/(√(5)-1) in the form of p√(5) +q, where p and q are integers. (4)

Question

DO NOT USE A CALCULATOR IN THIS QUESTION.

Express
`((4√(5)-2)^(2))/(√(5)-1)` in the form of
`p√(5) +q`, where p and q are integers. (4)

Answer 1

Hi,

Explanation:

`\frac{{(4√(5) -2)}^2}{√(5) -1} \\\\=(16*5+4-8√(5) )/(√(5) -1) \\\\=((84-8√(5))(√(5)+1) )/(5-1) \\\\=(44+76√(5) )/(4) \\\\=\boxed{=11+19√(5) }`