√(x+7)+√(x)=2

Question

√(x+7)+√(x)=2

tkhunny · Answer

Isolate a radical and square the whole thing!

Since we are acting foolishly and squaring things, we WILL have to check the results before we think we are done.

anonymous · Answer

Okay after that I got x=-x-3

tkhunny · Answer

That does not look right.

$\sqrt{x+7} + \sqrt{x} = 2$

Isolate a radical

$\sqrt{x+7} = 2 - \sqrt{x}$

Square things

$x+7 = 4 - 4\sqrt{x} + x$

Simplify

$7 = 4 - 4\sqrt{x}$

$3 = - 4\sqrt{x}$

You should have ended up with something like that.  There should still be an unresolved radical.  If both your radicals went away, something went horribly wrong.

anonymous · Answer

Ahhhhh I see how did you get the -4√x +x

tkhunny · Answer

The entire right side.

$(2 - \sqrt{x})^{2} = 2^{2} - 2(2)\sqrt{x} + \sqrt{x}^{2}$

Practice squaring binomials.  Useful skill.