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If $x + y + z = 1, xy + yz + zx = -26$ and $x^3 + y^3 + z^3 = 151$, then what will be the value of $xyz$? |
24 -30 -18 32 |
24 |
x + y + z = 1, xy + yz + zx = – 26, x3 + y3 + z3 = 151 x3 + y3 + z3 – 3xyz = (x + y + z)[(x + y + z)2 – 3 (xy + yz + zx)] = 151 – 3xyz = 1 [12 – 3 × ( – 26)] = 151 – 3xyz = 1 + 78 = 79 = 3xyz = 151 – 79 = 72 = xyz = 24 |
