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  • Determine x,y ,z belong to R such that 2x^2 +y^2 +2z^2-8x+2y-2xy+2xz-16z+35=0

Determine x,y ,z belong to R such that 2x^2 +y^2 +2z^2-8x+2y-2xy+2xz-16z+35=0

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Solution:  

            2x^2+y^2+2z^2-8x+2y-2xy+2xz-16z+35=0

      \ \ Rightarrow (x-y)^2+(x+z)^2+z^2-16z-8x+2y+35=0\ \ Rightarrow (x-y-1)^2+(x+z-3)^2+z^2-10z+25=0\ \ Rightarrow (x-y-1)^2+(x+z-3)^2+(z-5)^2=0

Thus ,   x-y-1=0,x+z-3=0hspace0.2cmand z=5\ \ herefore x=-2,y=-3 hspace0.2cmz=5

  Thus the solution is    x=-2,y=-3 hspace0.1cmand hspace0.2cmz=5.

Posted by

Deependra Verma

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