Chapter 6.7, Problem 31PPS

To determine

To Solve:

  $\sqrt{x-4}=\sqrt{2x-13}$

Answer to Problem 31PPS

x = 9

Explanation of Solution

Given Information:

Given equation:

  $\sqrt{x-4}=\sqrt{2x-13}$

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 $\sqrt{x-4}=\sqrt{2x-13}$

  $\begin{array}{l}\sqrt{x-4}=\sqrt{2x-13}\\ \Rightarrow {\left(\sqrt{x-4}\right)}^2={\left(\sqrt{2x-13}\right)}^2\mathrm{..........}[\text{Squaring both sides]}\\ \Rightarrow x-4=2x-13\\ \Rightarrow -4=2x-13-x\mathrm{..................................}[\text{Subtract x from each side]}\\ \Rightarrow -4=x-13\\ \Rightarrow 13-4=x\mathrm{............................................}[\text{Add 13 each side]}\\ \Rightarrow \text{9}=x\end{array}$

Check :

  

From the graph , it is verified that the solution of the given equation is x = 9.