If $x-y=15$ and $xy=4$, what is the value of $x^2+y^2$?
\((x-y)^2 = (x^2 + y^2) - 2xy\\ x^2 + y^2 = (x-y)^2 + 2xy = \\ 225+8 = 233\)
\((x-y)^2=(x^2+y^2)-2xy\)
Substituting our given numbers,
\(15^2=(x^2+y^2)-2(4), 225=(x^2+y^2)-8, x^2+y^2=233\)
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