Solving $ \sqrt{x - 4} + \sqrt{x - 7} = 1 $. I have the equation $ \sqrt{x - 4} + \sqrt{x - 7} = 1 $.
I tried to square both sides, but then I got a more difficult equation:
$$
2 x - 11 + 2 \sqrt{x^{2} - 11 x - 28} = 1.
$$
Can someone tell me what I should do next?

$$\sqrt{x-4}+\sqrt{x-7}=1<=>$$
$$-11+2\sqrt{(x-7)(x-4)}=12-2x<=>$$
$$4(x-7)(x-4)=(12-2x)^2<=>$$
$$4x^2-44x+112=4x^2-48x+144<=>$$
$$4x-32=0<=>$$
$$4(x-8)=0<=>$$
$$x-8=0<=>$$
$$x=8$$
BUT THIS SOLUTION IS INCORRECT SO THERE ARE NO SOLUTIONS!!!!!
