Algebra practice question for Railways, SSC. Review the correct answer and explanation, then continue with related practice below.
If x = (√5 + 2) (√5 − 2) and y = (√5 − 2) (√5 + 2), then find the value of x² + y².
Correct Answerसही उत्तर
A. 322 / 322
Explanationव्याख्या
On rationalising, x = (√5 + 2)²
(5 − 4) = 9 + 4√5 and y = (√5 − 2)²
(5 − 4) = 9 − 4√5.
Therefore, x + y = 18 and xy = 1.
Using x² + y² = (x + y)² − 2xy, we get x² + y² = 18² − 2(1) = 324 − 2 = 322.
परिमेयकरण करने पर x = (√5 + 2)²
(5 − 4) = 9 + 4√5 तथा y = (√5 − 2)²
(5 − 4) = 9 − 4√5।
अतः x + y = 18 और xy = 1।
सूत्र x² + y² = (x + y)² − 2xy का प्रयोग करने पर, x² + y² = 18² − 2(1) = 324 − 2 = 322 प्राप्त होता है।
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