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Find all solutions to the equation $\sqrt{3x+6}=x+2$. If there are multiple solutions, order them from least to greatest, separated by comma(s).

Guest Aug 17, 2017

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 #1
avatar+18552 
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Find all solutions to the equation \sqrt{3x+6}=x+2 (\(\sqrt{3x+6}=x+2\)).
If there are multiple solutions,
order them from least to greatest, separated by comma(s).

 

\(\begin{array}{|rcll|} \hline \sqrt{3x+6} &=& x+2 \quad & | \quad \text{square both sides} \\ 3x+6 &=& (x+2)^2 \\ 3x+6 &=& x^2+4x+4 \\ x^2 +x -2 &=& 0 \\ (x+2)(x-1) &=& 0 \\\\ x_1 &=& -2 \\ x_2 &=& 1 \\ \hline \end{array}\)

 

Solution Set: {-2,1}

 

Proof:
\(x=-2:\qquad \sqrt{3\cdot(-2)+6} = -2+2\quad \checkmark \\ x=1: \qquad \sqrt{3\cdot(1)+6} = 1+2 \quad \checkmark \)

 

laugh

heureka  Aug 17, 2017
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1+0 Answers

 #1
avatar+18552 
+1
Best Answer

Find all solutions to the equation \sqrt{3x+6}=x+2 (\(\sqrt{3x+6}=x+2\)).
If there are multiple solutions,
order them from least to greatest, separated by comma(s).

 

\(\begin{array}{|rcll|} \hline \sqrt{3x+6} &=& x+2 \quad & | \quad \text{square both sides} \\ 3x+6 &=& (x+2)^2 \\ 3x+6 &=& x^2+4x+4 \\ x^2 +x -2 &=& 0 \\ (x+2)(x-1) &=& 0 \\\\ x_1 &=& -2 \\ x_2 &=& 1 \\ \hline \end{array}\)

 

Solution Set: {-2,1}

 

Proof:
\(x=-2:\qquad \sqrt{3\cdot(-2)+6} = -2+2\quad \checkmark \\ x=1: \qquad \sqrt{3\cdot(1)+6} = 1+2 \quad \checkmark \)

 

laugh

heureka  Aug 17, 2017

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