Question

Find the value of x³+y³-12xy+64,whenx+y=-4.

Answer 1

Answer:

Here's the solution

Hope it helps

Answer 2

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GIVEN :

$x + y = - 4$

TO FIND :

${x}^{3} + {y}^{3} - 12xy + 64$

FORMULA TO BE USED :

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ \\ \\ i.e. \: \: \: \: \: \: \: \: \: \: \: \: \\ {a}^{3} + {b}^{3} = {( a+b )}^{3} - 3ab(a +b )$

SOLUTION :

${ x}^{3} + {y}^{3} - 12xy \: + 64 \\ \\ (using \: identity \: {a}^{3} + {b}^{3} = {(a +b )}^{3} - 3ab(a +b )) \\ \\ = {(x + y)}^{3} - 3xy(x + y) - 12xy + 64 \\ \\ = {( - 4)}^{3} - 3xy( - 4) - 12xy + 64 \\ \\ = - 64 + 12xy - 12xy + 64 \\ \\ = 0$

HENCE THE ANSWER WILL BE ZERO.

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