If xy=6 and x+x^2y+xy^2+y = 63, then x^2+y^2 =

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Solution

x^2y + y^2x + x +y=63

xy(x+y)+x+y=63(taking xy common)

6(x+y)+x+y=63 (xy= 6 ,given)

6x+6y+x+y=63

7x+7y=63

x+y=9

(x+y)2= x^2+2xy+y^2

(9)^2=x2+2(6)+y2

81= x^2+12+y^2

x^2+y^2=81-12

=69

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If xy=6 and x+x^2y+xy^2+y = 63, then x^2+y^2 =

x^2y + y^2x + x +y=63 xy(x+y)+x+y=63(taking xy common) 6(x+y)+x+y=63 (xy= 6 ,given) 6x+6y+x+y=63 7x+7y=63 x+y=9 (x+y)2= x^2+2xy+y^2 (9)^2=x2+2(6)+y2 81= x^2+12+y^2 x^2+y^2=81-12 =69

x^2y + y^2x + x +y=63

xy(x+y)+x+y=63(taking xy common)

6(x+y)+x+y=63 (xy= 6 ,given)

6x+6y+x+y=63

7x+7y=63

x+y=9

(x+y)2= x^2+2xy+y^2

(9)^2=x2+2(6)+y2

81= x^2+12+y^2

x^2+y^2=81-12

=69