Question
If x = (√13 + √12)/ (√13 - √12) and y = (√13 -
√12)/(√13 + √12), then find the value of 4x2 – xy + 4y2.Solution
4x2 – xy + 4y2 4(x2 + y2) – xy 4[(x + y)2 – 2xy] – xy 4(x + y)2 – 9xy ……..(1) x + y = [(√13 + √12)/(√13 - √12)] + [(√13 - √12)/(√13 + √12)] = [(√13 + √12)2 + (√13 - √12)2]/((√13)2 - (√12)2) = [13 + 12 + 2(√13)(√12) + 13 + 12 - 2(√13)(√12)]/2 = 25 xy= [(√13 + √12)/(√13 - √12)][(√13 - √12)/(√13 + √12)] = 1 From eq (1) => 4(25)2 - 9 = 2491
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