Question

the square root of x+2 minus the square root of 2x-3 equals to -1 what are the solutions for x?

Answer 1

is this your question?\[\sqrt{x+2}-\sqrt{2x-3}=-1\]

Answer 2

yea

Answer 3

ok, so what you need to do first is to rearrange this so that you get just one square root on the left-hand-side as follows:\[\sqrt{x+2}-\sqrt{2x-3}=-1\]\[\sqrt{x+2}=\sqrt{2x-3}-1\]now you can square both sides to get:\[x+2=(\sqrt{2x-3}-1)^2=2x-3-2\sqrt{2x-3}+1=2x-2-2\sqrt{2x-3}\]then rearrange this to get a zero on the right-hand-side as follows:\[x+2-2x+2+2\sqrt{2x-3}=0\]\[-x+4+2\sqrt{2x-3}=0\]we now want to try and do something to this so that we get a term like "2x-3" outside of the square root. so first, lets multiply this by -2 to get:\[2x-8-4\sqrt{2x-3}=0\]\[(2x-3)-5-4\sqrt{2x-3}=0\]this looks like a standard quadratic equation. so substitute:\[y=\sqrt{2x-3}\]to get:\[y^2-5-4y=0\]factorise to get:\[(y-5)(y+1)=0\]so y=5 or -1, which means:\[\sqrt{2x-3}=5\]or\[\sqrt{2x-3}=-1\]you should be able to solve these last two equations...