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![Which value for the constant
c makes
z=-(5)/(4) an extraneous solution in the following equation?
{:[sqrt(4z+9)=cz+8],[c=◻]:}](https://externalquestionsimg-a4fuc2b6e0gtdqge.z01.azurefd.net/external-question-images/images/images/ka/Algebra-2/Equations/Extraneous%20solutions/Q-29.png)
Which value for the constant makes an extraneous solution in the following equation?\begin{align*} \sqrt{4z+9} &= cz+8 \ c &= \square \end{align*}
Full solution
Q. Which value for the constant makes an extraneous solution in the following equation?\begin{align*}
\sqrt{4z+9} &= cz+8 \
c &= \square
\end{align*}
- Substitute : First, let's substitute into the left side of the equation to see what happens.
- Simplify expression: Now, let's simplify the expression inside the square root.
- Take square root: Next, we take the square root of .
- Substitute z: Now, let's substitute into the right side of the equation.
- Find value of c: We want to be an extraneous solution, which means the equation should not hold true when we substitute . Therefore, we need to find a value of such that:
- Isolate c in inequality: Let's solve for c by isolating it on one side of the inequality.
- Move terms to other side: Now, we'll move to the other side by adding to both sides.
- Subtract from both sides: Next, we'll subtract from both sides to isolate the term with on one side.
- Multiply both sides: To solve for , we'll multiply both sides by .
- Perform multiplication: Finally, we'll perform the multiplication to find the value of .
