Show that `(x^2+1)^2-x^2=0` has no real roots.

Options

A. four real roots
B. two real roots
C. no real roots
D. one real root

Explanation

To show that the equation \((x^2 + 1)^2 - x^2 = 0\) has no real roots, we will follow these steps:

### Step 1: Expand the equation
We start with the equation:
\[ (x^2 + 1)^2 - x^2 = 0 \]
We can expand \((x^2 + 1)^2\) using the identity \((a + b)^2 = a^2 + 2ab + b^2\):
...