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Question: If $x + y = 10$ and $x^2 + y^2 = 58$, find $x^3 + y^3$.$x + y = 10$$x^2 + y^2 = 58$We first find $xy$ using the identity:Now substitute into the identity for $x^3 + y^3$:x^3 + y^3 = (x + y)^3 - 3xy(x + y) = 10^3 - 3 \cdot 21 \cdot 10 = 1000 - 630 = 370oxed{370}Question: If $x + rac{1}{x} = 3$, what is the value of $x^3 + rac{1}{x^3}$?x^3 + rac{1}{x^3} = \left(x + rac{1}{x}ight)^3 - 3\left(x + rac{1}{x}