Question

A. Show all of your work to solve each equation and to check for extraneous solutions:4. [√(2x^2 - 1)]=x

Answer 1

x = 1

Explanation:

We have the following equation:

`√(2x^2-1)=x`

We solve for x:

`\begin{gathered} 2x^2-1=x^2 \\ \\ 2x^2-x^2=1 \\ \\ x^2=1 \\ \\ x=√(1)=\pm1 \\ \\ \text{ we check:} \\ x=1 \\ \\ √(2\left(1\right)^2-1)=1 \\ \\ √(2-1)=1 \\ \\ 1=1 \\ \\ x=-1\rightarrow\text{ true} \\ \\ √(2\left(-1\right)^2-1)=-1 \\ \\ √(2^-1)=-1 \\ \\ 1=-1\rightarrow\text{ false} \end{gathered}`

Therefore, the solution of the equation is x = 1