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)

asked Jan 11, 2024 121k views

5 votes

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)

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3 votes

Answer:

Hi,

Explanation:

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

Ivan Minakov answered Jan 17, 2024