If x = (√2+√1 )/(√2-√1), y = (√2-√1)/((√2+√1 )), find the value of (x²+y²)
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Correct answer: A
Explanation
Given:
x = (√2 + √1) / (√2 − √1)
y = (√2 − √1) / (√2 + √1)
By the formula:
(x + y)² = x² + y² + 2xy
√1 = 1
x = (√2 + 1) / (√2 − 1)
y = (√2 − 1) / (√2 + 1)
xy = 1
x + y = (√2 + 1)/(√2 − 1) + (√2 − 1)/(√2 + 1)
= [(√2 + 1)² + (√2 − 1)²] / [(√2 − 1)(√2 + 1)]
= (2 + 2√2 + 1 + 2 − 2√2 + 1) / (2 − 1)
= 6
(x + y)² = x² + y² + 2xy
6² = x² + y² + 2(1)
36 = x² + y² + 2
x² + y² = 34