A) \[-\]1
B) 1
C) \[-\]2
D) 2
Correct Answer: B
Solution :
[b] \[x+y+z=1,\,\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1,\,xyz=-\,1\] \[\frac{xy+zy+zx}{-\,1}=1\] \[xy+zy+zx=-\,1\] \[{{(x+y+z)}^{2}}=1\] \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2xy+2yz+2zx=1\] \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2\,\,(-\,1)=1\] \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=3\] \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-\,3xyz\] \[=(x+y+z)\,\,({{x}^{2}}+{{y}^{2}}+{{z}^{2}}+xy-\,yz-\,zx)\] \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}+3=4\] \[=4-\,3=1\]
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