Question

$\frac{2 - \sqrt{5} }{2 + \sqrt{5} } = a \sqrt{5 } + b$
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Answer 1

Answer:

a = (-4) and b = (-9)

Step-by-step explanation:

(2-√5)/(2+√5) × (2-√5)/(2-√5)

(2-√5)²/(2-√5)(2+√5)

(2)²+(√5)²+2(2)(√5)/(2)²-(√5)²

4+5+4√5/4-5

9+4√5/(-1)

=> (-9-4√5)

comparing with a√5+b,

-4√5-9 = a√5+b

-4√5+(-9) = a√5+b

now, a = (-4) and b = (-9).