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If x = (√6 − 1)/(√6 + 1) and y = (√6 + 1)/(√6 − 1), find (3x² + 5xy + 3y²)/(3x² − 5xy + 3y²).
A553/313
B663/313
C563/313
D563/303
Answer & Solution
Correct answer: C. 563/313
1. xy = 1; x + y = ((√6−1)² + (√6+1)²)/5 = (7−2√6 + 7+2√6)/5 = 14/5; so x² + y² = (14/5)² − 2 = 196/25 − 50/25 = 146/25.
2. Numerator = 3(146/25) + 5(1) = 438/25 + 125/25 = 563/25; denominator = 438/25 − 125/25 = 313/25.
3. Ratio = 563/313.
_Source: RRB Group D CEN-02/2018 PYQ, Q.82._
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