Question

If x+y=12,xy=27,find x3+y3

Answer 1

$We \:have \: x + y = 12 \:--(1)$

$xy = 27 \: --(2)$

/* By Algebraic Identity */

$\red{Value \:of \: x^{3} + y^{3}} \\= ( x + y )^{3} - 3xy ( x + y ) \\= (12)^{3} - 3 \times 27 \times 12 \\= 12(12^{2} - 81) \\= 12( 144 - 81 ) \\= 12 \times 63\\= 756$

Therefore.,

$\red{ Value \:of \: x^{3} + y^{3}}\green {= 756 }$

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