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2022 New Zealand MO
8
8
Part of
2022 New Zealand MO
Problems
(1)
\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
10/9/2022
Find all real numbers
x
x
x
such that
−
1
<
x
≤
2
-1 < x \le 2
−
1
<
x
≤
2
and
2
−
x
+
2
+
2
x
=
x
4
+
1
x
2
+
1
+
x
+
3
x
+
1
.
\sqrt{2 - x}+\sqrt{2 + 2x} =\sqrt{\frac{x^4 + 1}{x^2 + 1}}+ \frac{x + 3}{x + 1}.
2
−
x
+
2
+
2
x
=
x
2
+
1
x
4
+
1
+
x
+
1
x
+
3
.
.
algebra