Radical Equations with Two Radicals and a Constant Term
These types of equations can get quite complicated when solving by handing if the index of the radicals is any higher than \(2\) so we will stick to radical equations that involve two square roots and a constant term.
Steps for solving radical equations with two radicals and a constant term:
Example 1: Solve over the real numbers: \(\sqrt{x+4}-\sqrt{2x-9}=2\).
These types of equations can get quite complicated when solving by handing if the index of the radicals is any higher than \(2\) so we will stick to radical equations that involve two square roots and a constant term.
Steps for solving radical equations with two radicals and a constant term:
- Make sure the radicals are on opposite sides. Bring the constant term to the side that is less complicated.
- Square both sides. Isolate the remaining radical.
- Square both sides again.
- Solve the equation.
- Check for extraneous solutions.
Example 1: Solve over the real numbers: \(\sqrt{x+4}-\sqrt{2x-9}=2\).