If X + y + z equal to 1 xy + y z plus ZX equal to -1 x y z equal to -1 then x cube + y cube + z cube equal to
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Given
x+y+z=1,xy+yz+zx=−1 and xyz=−1
x
3
+y
3
+z
3
−3xyz=(x+y+z)(x
2
+y
2
+z
2
−xy−yz−zx)
x
3
+y
3
+z
3
−3(−1)=1(x
2
+y
2
+z
2
)−(−1)
x
3
+y
3
+z
3
+3=x
2
+y
2
+z
2
+1
x
3
+y
3
+z
3
+2=x
2
+y
2
+z
2
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