If x + y = 7 and xy = 12, find x² + y.

x + y = 7

⇒ y = 7-x …Equation (i)

xy = 12

Putting the value of y from above Equation (i) we get

x(7-x) = 12

⇒ 7x-x² = 12

⇒x²-7x + 12 = 0

Solving the above equation by the method of factorization we get

⇒ x²-4x-3x + 12 = 0

⇒x(x-4)-3(x-4) = 0

⇒(x-4)(x-3) = 0

x = 4,3

When x = 4, y = 3

⇒ x² + y = 19

When x = 3, y = 4

⇒ x² + y = 13