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Find the value of x^3-8y^3-36 x y-216 , ...

Find the value of `x^3-8y^3-36 x y-216 ,` when `x=2y+6.`

Text Solution

Verified by Experts

We have
`x^3-8y^3-36xy-216`
`=x^3+(-8y^3)+(-216)-36xy`
`=x^3+(-2y)^3+(-6)^3-3xx x xx (-2y)xx (-6)`
`=a^3+b^3+c^3 -3abc, " where " a=x, b=-2y and c=-6`
`=(a+b+c)(a^2+b^2+c^2-ab-bc -ca)`
`=(x-2y-6)(x^2+4y^2+36+2xy-12y+6x)`
`=0xx (x^2+4y^2+36+2xy-12xy-12y+6x)=0" " [because x-2y-6=0("given")]`.
Hence, `x^3-8y^3-36xy-216=0`.
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