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Find the value of x^3+y^3-12 x y+64 ,\ \...

Find the value of `x^3+y^3-12 x y+64 ,\ \ w h e n\ \ x+y=-4`

Text Solution

Verified by Experts

We have
`x^3+y^3-12xy+64`
` =x^3+y^3+4^3-3xx x xx y xx 4`
`=x^3+y^3+z^3-3xyz, " where " 4=z`
`=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)`
`= (x+y+4) (x^2 +y^2+16-xy-4y -4x) [because z =4]`
`=(-4+4)(x^2+y^2+16-xy-4y-4x) [because (x+y)=-4]`
` =0xx (x^2+y^2+16 -xy-4y-4x)=0`
Hence, `x^3+y^3-12xy+64=0`.
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