If a = (√5 + 1) / (√5 - 1) and b = (√5

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If a = (√5 + 1) / (√5 - 1) and b = (√5 - 1) / ( √5 + 1) then the value of (a² + ab + b²) / (a² - ab + b²) is ?

1. 3/4
2. 4/3
3. 3/5
4. 5/3

Correct Option: B

a = [(√5 + 1) / (√5-1)] x [(√5 + 1) / (√5 + 1)]
= (√5 + 1)² / (5 - 1)
= (5 + 1 + 2 √5) / 4
= (3 + √5) / 2

b = [(√5 - 1) / (√5 + 1)] x [(√5 - 1 ) / (√5 -1)]
= (√5 - 1 )² / (5 - 1)
= (5 + 1 - 2√5) / 4
= (3 - √5) / 2

Now a² + b² = [(3 + √5)² + (3 - √5)²] / 4
= [2 x (9 + 5 )] / 4
= 7

ab = 1

∴ (a² + ab + b²) / (a² - ab + b²)
= (7 + 1) / (7 - 1)
= 8/6
= 4 / 3