If x+y=11 and xy=15, find the value of x^2 + y^2

There is actually some tactics to this. I tried to find x and y first but they are very messy numbers but ...

We know ...

(x+y) ²=x²+2xy+y²

In this case, (x+y) ² = 11² = 121.

So, x²+2xy+y²=121

We also know that xy=15 and furthermore that 2xy=30.

x²+y² = 121-30 = 91

answer: 91