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Questions: Algebra BusinessCalculus
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Solve. \(\displaystyle \sqrt{x + 28}=\sqrt{x + 8} - 2\)
Squaring both sides gives \(\displaystyle x + 28=x - 4 \sqrt{x + 8} + 12\). Isolating the radical gives \(\displaystyle -4=\sqrt{x + 8}\) Squaring again gives \(\displaystyle 16=x + 8\). Solving for \(\displaystyle x\) gives \(\displaystyle x=8\). Checking the solution, \(\displaystyle x = 8\), in the original equation gives \(\displaystyle 6 = 2\) which is false so it is an extraneous solution and there is no solution.
\begin{question}Solve. $\sqrt{x + 28}=\sqrt{x + 8} - 2$
\soln{10cm}{Squaring both sides gives $x + 28=x - 4 \sqrt{x + 8} + 12$. Isolating the radical gives $-4=\sqrt{x + 8}$ Squaring again gives $16=x + 8$. Solving for $x$ gives $x=8$. Checking the solution, $x = 8$, in the original equation gives $6 = 2$ which is false so it is an extraneous solution and there is no solution.}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve. <img class="equation_image" title=" \displaystyle \sqrt{x + 28}=\sqrt{x + 8} - 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Csqrt%7Bx%20%2B%2028%7D%3D%5Csqrt%7Bx%20%2B%208%7D%20-%202%20" alt="LaTeX: \displaystyle \sqrt{x + 28}=\sqrt{x + 8} - 2 " data-equation-content=" \displaystyle \sqrt{x + 28}=\sqrt{x + 8} - 2 " /> </p> </p><p> <p>Squaring both sides gives <img class="equation_image" title=" \displaystyle x + 28=x - 4 \sqrt{x + 8} + 12 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2028%3Dx%20-%204%20%5Csqrt%7Bx%20%2B%208%7D%20%2B%2012%20" alt="LaTeX: \displaystyle x + 28=x - 4 \sqrt{x + 8} + 12 " data-equation-content=" \displaystyle x + 28=x - 4 \sqrt{x + 8} + 12 " /> . Isolating the radical gives <img class="equation_image" title=" \displaystyle -4=\sqrt{x + 8} " src="/equation_images/%20%5Cdisplaystyle%20-4%3D%5Csqrt%7Bx%20%2B%208%7D%20" alt="LaTeX: \displaystyle -4=\sqrt{x + 8} " data-equation-content=" \displaystyle -4=\sqrt{x + 8} " /> Squaring again gives <img class="equation_image" title=" \displaystyle 16=x + 8 " src="/equation_images/%20%5Cdisplaystyle%2016%3Dx%20%2B%208%20" alt="LaTeX: \displaystyle 16=x + 8 " data-equation-content=" \displaystyle 16=x + 8 " /> . Solving for <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle x=8 " src="/equation_images/%20%5Cdisplaystyle%20x%3D8%20" alt="LaTeX: \displaystyle x=8 " data-equation-content=" \displaystyle x=8 " /> . Checking the solution, <img class="equation_image" title=" \displaystyle x = 8 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%208%20" alt="LaTeX: \displaystyle x = 8 " data-equation-content=" \displaystyle x = 8 " /> , in the original equation gives <img class="equation_image" title=" \displaystyle 6 = 2 " src="/equation_images/%20%5Cdisplaystyle%206%20%3D%202%20" alt="LaTeX: \displaystyle 6 = 2 " data-equation-content=" \displaystyle 6 = 2 " /> which is false so it is an extraneous solution and there is no solution.</p> </p>