1.

Find the value of :`(1) x^3 + y^3 -12xy + 64` when `x+y+4=0``(2) x^3 -8y^3-36xy+216` when `x-2y+6=0`

Answer» (i) here we see that x+y+4=0
`therefore x^(3)+Y^(3)+(4)^(3)=3xy(4)`
[using idenity ,`a+b+c =0, "then" a^(3)+b^(3)+c^(3)=3abc`]
`12xy ….(i) ` Now , `x^(3)+y^(3)-12xy+64=x^(3)+64=x^(3)+y^(3)+64-12xy`
`=12xy-12xy =0`[fom Eq,(i) ]
(ii) here , we see that `x-2y-6=0`
`x^(3)+(-2)^(3)+(-6)^(3)=3x(-2y)(-6)`
[using i identity `a+b+c=0 "then " a^(3)+b^(3)+c^(3)=3abc`]
`implies x^(3)-8y^(3)-216=36xy`
Now , `x^(3)-8y^(3)-36xy-216` .....(i)
`=x^(3)-8y^(3)-216-36xy `
`=36xy-36xy=0` [from Eq.(i) ]


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