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
More Algebra Questions
31% of 3300 +659 = ?
?= √(4 × ∛(16 × √(4 × ∛(16 ×…… ∝)) ) )
60% of 500 + (729) 1/3 - ? = 72
∛857375 + ∛91125 = ? + √6889
1365 ÷ 15 + (? ÷ 5) = 62 × 3.5
Find the Value of
x= √(4 × ∛(16 × √(4 × ∛(16 ×…… ∝)) ) )
?2 = √20.25 × 10 + √16 + 32
36.76 + 2894.713 + 34965.11 =?
(2 ÷ 3) × (4 ÷ 12) × (? ÷ 10) × 45 × (1 ÷ 5) = (? ÷ 6) + (2 ÷ 5)
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