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Question

# If x2+xy+xz=135,y2+yz+xy=351 and z2+xz+yz=243, then x2+y2+z2=?

A
300
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B
275
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C
250
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D
225
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Solution

## The correct option is B 275x2+xy+xz=135........(i)y2+yz+xy=351........(ii)z2+xz+yz=243........(iii)Adding (i), (ii), (iii), we get,x2+y2+z2+2(xy+yz+xz)=729=>(x+y+z)2=272x+y+z=27........(iv)In equation (i),x2+xy+xz=135=>x(x+y+z)=135=>x×27=135=>x=5Similarly in equation (ii), we get,y2+yz+xy=351=>y(x+y+z)=351=>y×27=351=>y=13Again in equation (iii), we get,z2+xz+yz=243=>z(x+y+z)=243=>z×27=243=>z=9x2+y2+z2=52+132+92=275

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