Answer:
r = 5
Step-by-step explanation:
Solving radical equations often results in extraneous solutions. These can be avoided by using a graphing calculator for the solution.
<h3>Graph</h3>The attached shows that the value of r that makes both sides of the equation have the same value is r = 5.
<em>Check:</em>
√(5·5 -9) -3 = √(5 +4) -2 ⇒ 4 -3 = 3 -2 . . . true
<h3>Analytical solution</h3>Solution of an equation like this is typically done by isolating the radical expressions, then squaring the equation.
We can add 3, square the equation, then isolate the radical and square again:
Trying these values in the original equation, we get ...
√((5(9/4) -9) -3 = √(9/4 +4) -2 ⇒ 1.5 -3 = 2.5 -2 . . . . . false
√(5(5) -9) -3 = √(5 +4) -2 ⇒ 4 -3 = 3 -2 . . . . . true
The solution is r = 5.
