1.

If a,y and z are real numbers such that `x^2 + y^2 + 2 z^2 = 4x - 2z + 2yz - 5`, then the possible value of (x-y-z) is :

Answer» `x^2+y^2+2z^2 = 4x-2z+2yz-5`
`=>x^2+y^2+2z^2-4x-2z-2yz+5 = 0`
`=>(x-2)^2+(y-z)^2+(z+1)^2 = 0`
We know, `a^2+b^2+c^2 = 0` implies `a = b = c= 0`
`:. x-2 = 0=> x = 2`
`z+1 = 0=> z = -1`
`y-z = 0 => y = z => y = -1`
`:. x-y-z = 2+1+1 = 4`


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