One solution to the given equation can be written as $1+\sqrt{k}$, where $k$ is a constant. What is the value of $k$ ?
A. 8
B. 10
C. 20
D. 40

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StudyXY · Accepted Answer

: First, we need to square both sides of the equation since the given solution is in the form $1+\sqrt{k}$. : Expand the left side of the equation using the formula for squaring a binomial. : Since the given solution is $1+\sqrt{k}$, the right side of the equation should also have a $1$ when we isolate the square root term. : Subtract $1$ from both sides to simplify the equation. : Move the $k$ term to the right side. : Square both sides again to eliminate the square root. : Simplify both sides of the equation. : Rearrange the equation to form a quadratic equation. : Factor the quadratic equation. : Solve for $k$ by setting each factor equal to zero and finding the corresponding solutions. Choice (D) is correct.

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QuestionAnatomy and Physiology

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Step 1
: First, we need to square both sides of the equation since the given solution is in the form $1 +\sqrt{k}$.

Step 2
: Expand the left side of the equation using the formula for squaring a binomial.

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