Question
If [8(x + y)3 – 27(x – y)3] ÷
(5y – x) = Ax2 + Bxy + Cy2, then the value of (A2 - 2B + 3C) is:Solution
=> [8(x + y)3 – 27(x – y)3] ÷ (5y – x) = Ax2 + Bxy + Cy2 => [{2(x + y)}3 – {3(x – y)3}] ÷ (5y – x) = Ax2 + Bxy + Cy2 => {2(x + y)} – {3(x – y)} [{2(x + y)}2 + 2(x + y)3(x – y) + {3(x – y)}2] ÷ (5y – x) = Ax2 + Bxy + Cy2 => (5y – x) [4x2 + 4y2 + 8xy + 6x2 – 6y2 + 9x2 + 9y2 – 18xy] ÷ (5y – x) = Ax2 + Bxy + Cy2 => 19x2 – 10xy + 7y2 = Ax2 + Bxy + Cy2 On comparing => A = 19, B = -10 and C = 7 => (A2 - 2B + 3C) = 192 - 2 × - 10 + 3 × 7 = 402
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