Review question

# How many solutions are there to $(x^2+1)^{10} = 2x - x^2 - 2$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9754

## Suggestion

The equation $(x^2+1)^{10} = 2x - x^2 - 2$

1. has $x=2$ as a solution;

2. has no real solutions;

3. has an odd number of real solutions;

4. has twenty real solutions.

Could we draw the graphs of the functions on the left and right hand sides of the equation?

Can we write the quadratic on the right hand side in a different (more useful) form?