Question - Solving Radical Equation for p
Solution:
To solve the equation involving the radical, we want to isolate p. Given the equation from the image:$$\sqrt{\frac{2p+1}{t}} = 3$$First, square both sides of the equation to eliminate the square root:$$\left( \sqrt{\frac{2p+1}{t}} \right)^2 = 3^2$$This simplifies to:$$\frac{2p+1}{t} = 9$$Next, multiply both sides by t to remove the denominator:$$2p+1 = 9t$$Subtract 1 from both sides to isolate the term with p:$$2p = 9t - 1$$Finally, divide both sides by 2 to solve for p:$$p = \frac{9t - 1}{2}$$Therefore, the value of p in terms of t is:$$p = \frac{9t - 1}{2}$$
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