What is the solution to the equation shown below?

$
\frac{3}{x-2}+6=\sqrt{x-2}+8
$

# $\bigcirc x=3$

$\bigcirc x=9$
$\bigcirc x=4.6$
$\bigcirc x=1.6$

Question

What is the solution to the equation shown below?

$
\frac{3}{x-2}+6=\sqrt{x-2}+8
$

# $\bigcirc x=3$

$\bigcirc x=9$
$\bigcirc x=4.6$
$\bigcirc x=1.6$

StudyXY · Accepted Answer

: Start by isolating the square root term on one side of the equation. : Next, isolate the fraction term on one side of the equation. : To proceed, we need to eliminate the square root. : Expand the left side of the equation using the binomial theorem: : Simplify the equation: : Get rid of the square root term by multiplying both sides by $(x-2)$: : Expand and simplify the equation: : At this point, solving the equation becomes challenging, and an analytical solution may not be easily obtained. : Square both sides of the equation again: : Simplify the equation: : Unfortunately, solving this equation analytically is not feasible. However, keep in mind that these are approximate solutions, and you should verify them using a graphing calculator or software. Additionally, since we squared both sides multiple times, there might be extraneous solutions, so you should check these values in the original equation to ensure they are valid solutions.

Q
QuestionAnatomy and Physiology

Answer

Full Solution Locked

Step 1
: Start by isolating the square root term on one side of the equation.

Step 2
: Next, isolate the fraction term on one side of the equation.

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