Question

X+y=11, x.y=18 so what is the x^2 + y^2?

Answer 1

Let's begin with a basic formula
$(x+y)^{2} = x^{2} + 2xy + y^{2}$

so since we know the value of x + y and xy let's place those values inside the equation.

If xy=18, 2xy=36

$11^{2}=x^{2} + 36 + y^{2}$

$121=x^{2}+y^{2}+36$

$85=x^{2} + y^{2}$ 

Answer 2

Another way to look at it

Solve xy = 18 and get y = (1/x)18

plug into other eq get

x + (1/x)18 = 11

multiply both sides by x get 

x² -11x +18 = 0

find roots 

x = 2 or 9

You can use the same method to find that y is either 2 or 9. You do not have enough information to know which is which so x² + y² is either 2² + 9² or 9² + 2²

in either case the answer is 85