A) 3
B) 4
C) 8
D) 16
Correct Answer: A
Solution :
(a): \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}-6=0\] \[\Rightarrow {{x}^{2}}+\frac{1}{{{x}^{2}}}-2+{{y}^{2}}+\frac{1}{{{y}^{2}}}-2+{{z}^{2}}+\frac{1}{{{z}^{2}}}-2=0\] \[\Rightarrow {{\left( x-\frac{1}{x} \right)}^{2}}+{{\left( y-\frac{1}{y} \right)}^{2}}+{{\left( z-\frac{1}{z} \right)}^{2}}=0\] \[\Rightarrow \left( x-\frac{1}{x} \right)=0\therefore {{x}^{2}}-1=0\Rightarrow x=\pm 1\] Similarly \[y=\pm 1,z=\pm 1\,\,\therefore {{x}^{2}}+{{y}^{2}}+{{z}^{2}}=1+1+1=3\]You need to login to perform this action.
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