I am not too sure on how to actually solve this radical equation been stuck on it for a while the equation is:
\sqrt{2x+6} - \sqrt{x+4} =1
any help would be awesome
thanks in advance
I would first rewrite it as $\displaystyle \sqrt{2x+6}=1+\sqrt{x+4}$.
Squaring both sides, foiling and simplifying yields: $\displaystyle 2x+6=2\sqrt{x+4}+x+5$ (Verify)
Now, get everything but the radical on the other side of the equation: $\displaystyle \frac{x+1}{2}=\sqrt{x+4}$.
Square both sides again to get $\displaystyle \tfrac{1}{4}(x^2+2x+1)=x+4 \implies x^2-2x-15=0$ (Verify)
Now solve this quadratic equation for x to get two possible answers. Then test for possible extraneous solutions by plugging them into the original equation.
I hope this helps!