Solving radical equations

When solving radical equations we isolate the radical, and then square both sides of the equation. We must always check our answers in the original equation, because squaring both sides of an equation sometimes generates an equation that has roots that are not roots of the original equation.

Example

We are to solve the following radical equation:

$\sqrt{(1+x^{2}-x)}-x=0$

First we isolate our radical:

$\sqrt{(1+x^{2}-x)}=x$

Then we square both sides and solve our equation:

$\\ 1+x^{2}-x=x^{2}\\ 1-x=0\\ 1=x$

Lastly we plug our x into our original equation to check:

$\\ \sqrt{(1+1^{2}-1)}-1=0\\ \sqrt{1}-1=0\\ 1=1$

The solution checks.

Videolesson: solve the following radical expression

$\sqrt{x-2}=\sqrt{2}-\sqrt{x}$

Next Class: Polynomials and radical expressions, Complex numbers

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