यदि `x+y+z=6` और `x^(2)+y^(2)+z^(2)=20` है तो `x^(3)+y^(3)+z^(3)-3xyz` का मान ज्ञात करें।

Options

A. 64
B. 70
C. 72
D. 76

Answer

C

Explanation

`x+y+z=6`
`x^(2)+y^(2)+z^(2)=20`
`implies (x+y+z)^(2)=(6)^(2)`
`implies x^(2)+y^(2)+z^(2)+2(xy+yz+zx)=36`
`implies 20+2(xy+yz+zx)=36`
`implies 2(xy+yz+zx)=16`
`xy+yz+zx=8`
`implies x^(3)+y^(3)+z^(3)-3xyz=`
`(x+y+z)(x^(2)+y^(2)+z^(2)-xy-zx-yz)`
`implies x^(3)+y^(3)+z^(3)-3xyz=6(20-8)`
`=6xx12=72`