A) 2
B) 3
C) 4
D) None of these
Correct Answer: C
Solution :
Given \[{{x}^{2}}+{{y}^{2}}-{{z}^{2}}-64=-2(xy-yz-xz)\] Now, \[{{\left[ x+y+{{(-z)}^{2}} \right]}^{2}}=\,{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+\,2(xy-yz-zx)\] \[(3z-{{z}^{2}}={{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2(xy-yz-zx)\] \[-2(xy-yz-zx)=({{x}^{2}}+{{y}^{2}}+{{z}^{2}})-{{(2z)}^{2}}\] From (i) and (ii), we get: \[(2x)2=64\] \[4{{z}^{2}}=64\Leftrightarrow {{z}^{2}}=16\Leftrightarrow z=4\]
You need to login to perform this action.
You will be redirected in
3 sec
