x*y= 8 ... (i)

x^{2}y + x y^{2}^{ }+^{ }x + y= 54 ... (ii)

If x*y = 8

Then, x^{2}y = 8x [multiply x in both the sides of equation 1]

& x y^{2}^{ }= 8y [multiply y in both the sides of equation 1]

Thus, equation 2 can also be written as,

8x + 8y + x + y = 54

=> 9x + 9y = 54

=> x + y = 6

Now,

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

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

Therefore** x**^{2} + y^{2} = 36- 2*8 ie. 20