We want to find and check the solution of the given radical equation.
Finding the Solution
The first step in solving this equation is squaring both sides. Then, once the radicals are gone, we will solve for the variable using the Properties of Equality.
Now, we need to check whether our solution is extraneous. To check our solution, we will substitute 6 for v into the original equation. If we obtain a true statement, the solution is not extraneous. If we obtain a false statement, the solution is extraneous.
We obtained a true statement, so v=6 is a solution to the equation.
Alternative Solution
Using a Graphing Calculator
Another way to solve this equation is by using a graphing calculator. We will draw separate graphs for each side of the equation and then find the x-value of the point of intersection.
Graphing the Functions
Because graphing calculators always need functions to be written in terms of an x-variable, we need to begin by rewriting the given equation in terms of x. sqrt(2v-5)=sqrt(v/3+5)
⇓
sqrt(2 x-5)=sqrt(x/3+5)
Now, we need to create functions using the left-hand and right-hand side of the new version of our equation.
lcl
sqrt(2x-5) &⇒ &y=sqrt(2x-5)
sqrt(x/3+5) &⇒ &y=sqrt(x/3+5)
We first press the Y= button and type one function in one of the rows and the second function in another. Having written functions, we can push GRAPH to draw them.
Intersection Point
Having graphed the functions, we are ready to find the intersection point. By pressing 2ND and then CALC, we can select the option intersect.
Then the calculator will ask for the first and second curve as well as a guess. After that, the x-value of the point of intersection should be shown.
The x-value of the point of intersection is 6. Therefore, moving back to the original variable, v=6 is a solution to the given equation, as we found earlier algebraically.
