CBSE Class 9 Answered
If x +
y + z = 1, xy + yz + zx = -1 and xyz = -1 then find the value of x3
+ y3 + z3.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
Since (x + y + z)2 = x2 + y2 + z2 - 2xy - 2yz - 2zx
Or, 1 = x2 + y2 + z2 - 2 x -1
Or, 1 = x2 + y2 + z2 + 2
Or, x2 + y2 + z2 = -1
Now,
x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)
x3 + y3 + z3 = 3xyz + (x + y + z) (x2 + y2 + z2 - xy - yz - zx)
= -3 + 1(-1 + 1)
x3 + y3 + z3 = -3.
Answered by | 04 Jun, 2014, 03:23: PM
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