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?

squaring gives
$$x-4+x-7+2\sqrt{x-4}\sqrt{x-7}=1$$
$$\sqrt{x-4}\sqrt{x-7}=12-2x$$
$$(x-4)(x-7)=36+x^2-12x$$
$$x=8$$
but $8$ fulfills not our equation.
