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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 = 370
oxed{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}