Question

if xy=6 & x²y+xy²+x+ y=63 then x²+y²=?

Answer 1

$xy = 6 \\ {x}^{2} y + x {y}^{2} + x + y = 63 \\ xy(x + y) + (x + y) = 63 \\ (x + y)(xy + 1) = 63 \\ (x + y)(6 + 1) = 63 \\ x + y = 9$


(x+y)^2=x^2+y^2+2xy
81=x^2+y^2+2(6)
x^2+y^2=81-12
x^2+y^2=69
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Answer 2

=>{x}^{2}y+x+x{y}^{2}+y=63
=>x(xy+1)+y(xy+1)=63
=>(xy+1)(x+y)=63
=>7(x+y)=63
=>(x+y)=9


{x+y}^{2}={x+y}^{2}+2xy
=>{9}^{2}+2.6
=>81+12
=>63