Question

find the value of x3+y3-12xy+64, when x+y=-4

Answer 1

$\textbf{Given:}$

$x+y=-4$

$\textbf{To find:}$

$\text{The value of x^3+y^3-12xy+64 }$

$\textbf{Solution:}$

$\text{We know that,}$

$\textbf{If \bf\,a+b+c=0 then}$

$\bf\,a^3+b^3+c^3=3\,abc$

$\text{Consider,}$

$x+y=-4$

$\implies\,x+y+4=0$

$\text{Then,}$

$x^3+y^3+4^3=3\,xy(4)$

$x^3+y^3+64=12xy$

$\implies\,x^3+y^3-12xy+64=0$

$\textbf{Answer:}$

$\textbf{The value of \bf\,x^3+y^3-12xy+64 is 0}$

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