If x + y + z = 9, xyz = -336 and x 2 + y 2 + z 2 = 149 then find the v
| If x + y + z = 9, xyz = -336 and x2 + y2 + z2 = 149 then find the value of (x3+y3+z3).
A. 649
B. 639
C. 659
D. 637
Right Answer is: B
SOLUTION
Since we know that, (x+y+z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
81 = 149 + 2(xy+yz+zx)
-68 = 2(xy+yz+zx) or
(xy + yz + zx) = -34
Also, x3 + y3 + z3 – 3xyz = (x+y+z)(x2+y2+z2-xy-yz-zx)
x3+y3+z3 – 3(– 336) = 9[149 – (-34)]
x3+y3+z3 + 1008 = 9[149 + 34]
x3+y3+z3 = 1647 – 1008
x3+y3+z3 = 639.
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If x + y + z = 9, xyz = -336 and x 2 + y 2 + z 2 = 149 then find the v