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