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If x + y + z = 2, xy + yz + zx = -11, and xyz = -12, then what is the value of x3 +y3 +z3 ? |
36 38 40 42 |
38 |
x3 + y3 + z3 – 3xyz = (x + y +z) [(x + y + z)2 – 3(xy + yz + zx)] = x3 + y3 + z3 – 3 × (–12) = 2[22 – 3 × (– 11)] = x3 + y3 + z3 + 36 = 2[4 + 33] = x3 + y3 + z3 + 36 = 2 × 37 = x3 + y3 + z3 = 74 – 36 = 38 |
