JAMB 1985 · UME · Q20

At what real value of $x$ do the curves $y = x^3 + x$ and $y = x^2 + 1$ intersect?

Worked solution (try it first)

The curves meet where the $y$ -values are equal: $x^3 + x = x^2 + 1$ , so $x^3 - x^2 + x - 1 = 0$ .
Group the terms: $x^2(x - 1) + (x - 1) = 0$ , so $(x - 1)(x^2 + 1) = 0$ .
$x^2 + 1$ is always positive, so the only real solution is $x = 1$ , option E.