APFIVE Solving a Radical Equation in Quadratic Form
Solve for x in the equation
$$\sqrt{x+7}+\frac{2}{\sqrt{x+7}}=5.$$
(Use the substitution $$u=\sqrt{x+7}$$ and then solve for x.)
| u = √(x+7) | Equation Form |
|---|---|
| u | u + 2/u = 5 |
| Leads to: u² - 5u + 2 = 0 |
A
$$\left(\frac{5\pm\sqrt{17}}{2}\right)^2-7$$
B
$$\frac{5+\sqrt{17}}{2}-7$$
C
$$7-\left(\frac{5\pm\sqrt{17}}{2}\right)^2$$
D
$$\left(\frac{5-\sqrt{17}}{2}\right)^2-7$$
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