Question

I need algebra help, sqrt2x+6 - sqrtx-1 = 2

Answer 1

\[\sqrt{2x+6} - \sqrt{x-1} =2\]

Answer 2

Slightly differnet question, but should help you to know how to get to your answer
http://openstudy.com/study#/updates/51947e7ce4b0d270317f7d6f

Answer 3

Condition:\(\Large \begin{cases} 2x+6\ge 0 \\ x-1\ge 0 \end{cases}\Leftrightarrow \begin{cases} x\ge 3 \\ x\ge 1 \end{cases}\Rightarrow x\ge 3\)

\(\Large \sqrt{2x+6}-\sqrt{x-1}=2 \Leftrightarrow \sqrt{2x+6}=2+\sqrt{x-1}\)
\(\Large \Rightarrow (\sqrt{2x+6})^2=(2+\sqrt{x-1} )^2\)
\(\Large \Rightarrow 2x+6=4+4\sqrt{x-1} +x-1\)
\(\Large \Leftrightarrow 4\sqrt{x-1}=x+3\)
\(\Large \Rightarrow (4\sqrt{x-1})^2=(x+3)^2\)
\(\Large \Leftrightarrow 16(x-1)=x^2+6x+9\)
\(\Large \Leftrightarrow 16x-16=x^2+6x+9\)
\(\Large \Leftrightarrow x^2-10x+25=0\)
\(\Large \Leftrightarrow x=5\) (satisfy condition)