Solve the equation in the following question Solve the equation $$\sqrt{x+1}+\sqrt{2-x}+2=x^2+2x$$
I tried with squaring both sides, but I got confused, any help will be thankful.

You'll want just the terms with square roots on one side before you square both sides:
$$\sqrt{x+1}+\sqrt{2-x}=x^2+2x -2$$
Squaring, then simplifying so that again only the terms with square roots are on the left,
$$
(x+1) + 2\sqrt{x+1}\sqrt{2-x} + (2-x) = x^4+4x^3-8x+4\\
2\sqrt{x+1}\sqrt{2-x} = x^4+4x^3-8x+1\\
$$
Squaring again,
$$
4(x+1)(2-x) = x^8+8x^7+16x^6-16x^5-62x^4+8x^3+64x^2-16x+1\\
x^8+8x^7+16x^6-16x^5-62x^4+8x^3+68x^2-20x-7=0
$$
At this point I would throw my hands in the air and ask Wolfram Alpha, which tells me that there are four solutions; checking them in the original system, only one of them works: $x \approx 1.31295$.
What is the context of this problem? It would be extremely difficult to solve this by hand.
