Question

If xy=8 and x²y+xy²+X+y=54 then find x²+y²=

Answer 1

Explanation:

given

$x {y}^{2} + {x}^{2} y + x + y = 54$

$x + y + xy(x + y) = 54$

$(x + y)(xy + 1) = 54$

$xy = 8$

$(x + y)(8 + 1) = 54$

$(x + y)(9) = 54$

$x + y = 6$

SQUARING ON BOTH SIDES

$(x + y) ^{2} = {6}^{2}$

${x}^{2} + {y}^{2} + 2xy = 36$

${x}^{2} + {y}^{2} + (2 \times 8) = 36$

${x}^{2} + {y}^{2} + 16 = 36$

${x}^{2} + {y}^{2} = 20$

Answer 2

use the identity given in the question and try your self