यदि `x^(2)+y^(2)+z^(2)=2(x+z-1)` है तो `x^(3)+y^(3)+z^(3)=?`

Options

A. -1
B. 2
C. 0
D. 1

Answer

B

Explanation

Given `x^(2)+y^(2)+z^(2)=2(x+z-1)`
Find `x^(3)+y^(3)+z^(3)=?`
`implies x^(2)+y^(2)+z^(2)=2(x+z-1)`
`implies x^(2)+y^(2)+z^(2)=2x+2z-2`
`implies x^(2)+y^(2)+z^(2)=2x+2z-1-1`
`implies (x^(2)+1-2x)+y^(2)+(z^(2)+1-2z)=0`
`implies (x-1)^(2)+y^(2)+(z-1)^(2)=0`
`implies (x-1)^(2)=0`
`implies x=1`
`implies y^(2)=0`
`implies y=0`
`implies (z-1)^(2)=0`
`implies z=1`
Value substituted in question,
`implies x^(3)+y^(3)+z^(3)`
`implies 1^(3)+0+1^(3)`
`implies 2`