यदि `x+y+z=6` और `xy+yz+zx=10` तो `x^(3)+y^(3)+z^(3)-3xyz` का मान क्या होगा?

Options

A. 36
B. 40
C. 42
D. 48

Answer

A

Explanation

Given
`implies x+y+z=6`
`implies xy+yz+zx=10`
To find `x^(3)+y^(3)+z^(3)-3xyz=?`
`implies` Using formula.
`implies (x+y+z)^(2)=x^(2)+y^(2)+z^(2)+2`
`(xy+yz+zx)`
`implies 6^(2)=x^(2)+y^(2)+z^(2)+xx10`
`implies 36=x^(2)+y^(2)+z^(2)+20`
`implies x^(2)+y^(2)+z^(2)=16`
`implies x^(2)+y^(2)+z^(2)-3xyz=`
`(x+y+z)[x^(2)+y^(2)+z^(2)-xy-yz-zx]`
`=6[16-(xy)+yz+zx)]`
`=6[16-10]=6xx6=36`