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प्रश्न
If 2x – 3y – 4z = 0, then find 8x3 – 27y3 – 64z3
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उत्तर
We know x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
x3 + y3 + z3 = (x + y + z) (x2 + y2 + z2 – xy – yz – zx) + 3xyz
8x3 – 27y3 – 64z3 = (2x)3 + (– 3y)3 + (– 4z)3
= (2x – 3y – 4z) [(2x)2 + (– 3y)2 + (– 4z)2 – (2x)(– 3y) – (– 3y)(– 4z) – (– 4z)(2x)] + 3(2x)(– 3y)(– 4z)
= 0 (4x2 + 9y2 + 16z2 + 6xy – 12yz + 8xz) + 72xyz
= 72xyz
8x3 – 27y3 – 64z3 = 72xyz
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