Chapter 7.7, Problem 29PPS

To determine

To Solve:

  $6+\sqrt{4x+8}=9$

Answer to Problem 29PPS

x = 0.25

Explanation of Solution

Given Information:

Given equation:

  $6+\sqrt{4x+8}=9$

Concept Used :

Solve Radical equations:

• Isolate the radical on one side of the equation.
• Raise each side of the equation to a power equal to the index of the radical to eliminate the radical .
• Solve the resulting polynomial equation.Check your results.
• When solving radical equations, the result may be a number that does not satisfy the original equation . Such a number is called an extraneous solution.

Calculation:

Given $6+\sqrt{4x+8}=9$

  $\begin{array}{l}6+\sqrt{4x+8}=9\\ \Rightarrow \sqrt{4x+8}=9-\mathrm{6..........................}[\text{Subtract 6 from each side]}\\ \Rightarrow \sqrt{4x+8}=3\\ \Rightarrow {\left(\sqrt{4x+8}\right)}^2=3^2\\ \Rightarrow 4x+8=9\\ \Rightarrow 4x=9-\mathrm{8..................................}[\text{Subtract 8 from each side]}\\ \Rightarrow \text{4x=1}\\ \Rightarrow \frac{4x}{4}=\frac{1}{4}\mathrm{.....................................}[\text{Divide each side by 4]}\\ \Rightarrow \text{x=}\frac{1}{4}\end{array}$

Check :

  

So, from the graph , it is verified that the solution is x = 0.25