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\sqrt{2 - x}+\sqrt{2 + 2x} =\sqrt{(x^4 + 1)/(x^2 + 1)}+ (x + 3)/(x + 1)

Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p8

October 9, 2022
algebra

Problem Statement

Find all real numbers xx such that −1<x≤2-1 < x \le 2 and 2−x+2+2x=x4+1x2+1+x+3x+1.\sqrt{2 - x}+\sqrt{2 + 2x} =\sqrt{\frac{x^4 + 1}{x^2 + 1}}+ \frac{x + 3}{x + 1}. .
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