Question
If (54√2 x³ +24√3
y³)÷(√18 x + √12 y) = Ax² + By² + Cxy, then what is the value of A² - (B² + C²)?Solution
If (54√2 x³ +24√3 y³) ÷ (√18 x + √12 y) = Ax² + By² + Cxy We know that, x³ + y³ = (x + y) (x² + y² - ab) => (54√2 x³ +24√3 y³) / (√18 x + √12 y) => [(√18 x + √12 y) (√18 x² + √12 y² - √18×12 xy)]/(√18 x + √12 y) => (√18 x² + √12 y² - √18×12 xy) => Ax² + By² + Cxy Now, => A = 18, B = 12 and C = -6√6 Putting value of A,B and C we get, => A² - (B² + C²) = 324 - (144 + 216) = -36
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