CBSE Class 9 Answered
If
x + y + z = 1, xy + yz + zx = -1 and xyz = -1 find the value of x3+y3+z3.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
Identity:x3 +y3 +z3 -3xyz = (x+y+z)( x2 +y2 +z2 -xy-yz-zx)
Since x + y + z = 1, xy + yz + zx = -1and xyz= -1,
Putting values, we get:
So 
Now
(x+y+z)2 = x2 +y2 +z2 +2xy +2yz +2zx
12 = x2 +y2 +z2 +2(-1)
x2 +y2 +z2 = 3
Put in eq (i)
x3 +y3 +z3 =3-2 = 1
Answered by | 04 Jun, 2014, 03:23: PM
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