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If x = (√5 + 1)/(√5 - 1) and y = (√5 - 1)/(√5 + 1), then find the value of x2 - y2.
- A√5
- B2√5
- C3√5
- D4√5
Answer not set
Discussion 1
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CCommunity
x = (√5 + 1)/(√5 - 1)
⇒ x = [(√5 + 1)/(√5 - 1)] × [(√5 + 1)/ (√5 + 1)] = (3 + √5)/2
And, y = (√5 - 1)/(√5 + 1)
⇒ y = [(√5 - 1)/(√5 + 1)] × [(√5 - 1)/ (√5 - 1)] = (3 - √5)/2
∴ x2 - y2 = (x + y) (x - y) = 3 × √5 = 3√5
⇒ x = [(√5 + 1)/(√5 - 1)] × [(√5 + 1)/ (√5 + 1)] = (3 + √5)/2
And, y = (√5 - 1)/(√5 + 1)
⇒ y = [(√5 - 1)/(√5 + 1)] × [(√5 - 1)/ (√5 - 1)] = (3 - √5)/2
∴ x2 - y2 = (x + y) (x - y) = 3 × √5 = 3√5