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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

User UberJumper
by
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1 Answer

5 votes

ANSWER:

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

User Gareth Simpson
by
8.3k points

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