Question

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

Answer 1

Answer:

=>{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

Answer 2

Given, xy = 6

x²y + xy² + 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 = x² + y² + 2xy

➪81 = x² + y² + 2(6)

➪x² + y² = 81 - 12

➪x² + y² = 69

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