Answered

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

Sagot :

ANSWER:

x = 1

STEP-BY-STEP EXPLANATION:

We have the following equation:

[tex]\sqrt{2x^2-1}=x[/tex]

We solve for x:

[tex]\begin{gathered} 2x^2-1=x^2 \\ \\ 2x^2-x^2=1 \\ \\ x^2=1 \\ \\ x=\sqrt{1}=\pm1 \\ \\ \text{ we check:} \\ x=1 \\ \\ \sqrt{2\left(1\right)^2-1}=1 \\ \\ \sqrt{2-1}=1 \\ \\ 1=1 \\ \\ x=-1\rightarrow\text{ true} \\ \\ \sqrt{2\left(-1\right)^2-1}=-1 \\ \\ \sqrt{2^-1}=-1 \\ \\ 1=-1\rightarrow\text{ false} \end{gathered}[/tex]

Therefore, the solution of the equation is x = 1

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