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Question

# Find x2+y2+z2 if x2+xy+xz=135,y2+yz+yx=351 and z2+zx+zy=243.

A
225
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B
250
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C
275
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D
300
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Solution

## The correct option is B 275Given : x2+xy+xz=135 --- ( 1 ) ,y2+yz+yx=351 --- ( 2 )Andz2+zx+zy=243 --- ( 3 )Now we add equation 1 , 2 and 3 and getx2+y2+z2+2xy+2yz+2zx=729(x+y+z)2=729 ( We know : (x+y+z)2=x2+y2+z2+2xy+2yz+2zx)(x+y+z)2=272x+y+z=27 --- ( 4 )Now we take equation 1 : x2+xy+xz=135x(x+y+z)=135 , Substitute value from equation 4 and get 27x=135x=5And we take equation 2 :y2+yz+yx=351y(x+y+z)=351 , Substitute value from equation 4 and get 27y=351y=13And we take equation 3 : z2+zx+zy=243z(x+y+z)=243 , Substitute value from equation 4 and get 27z=243z=9Therefore,Value of x2+y2+z2=52+132+92=25+169+81=275

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