# Algebra Examples

Prove that a Root is on the Interval
,
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
The Intermediate Value Theorem states that, if is a real-valued continuous function on the interval , and is a number between and , then there is a contained in the interval such that .
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Calculate .
Simplify each term.
Remove parentheses around .
Raising to any positive power yields .
Multiply by to get .
Subtract from to get .
Calculate .
Simplify each term.
Remove parentheses around .
Raise to the power of to get .
Multiply by to get .