if (x,y) is solution set of system of equations x y = 8 and x²y + x y²+x+y=54 then x²+y²=

x*y= 8 ... (i)
x²y + x y² +^​ x + y= 54 ... (ii)

If x*y = 8
Then, x²y = 8x  [multiply x in both the sides of equation 1]
      & x y² = 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
x²+ y² + 2xy  = 36

Therefore x² + y² = 36- 2*8 ie. 20