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Given that $x$ is positive and less than 1, which of the following numbers is the largest?

$x^2 + x$, $x^2$, $x^3$, $x^3 + x^2$, $x^4$.
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

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