<s>[INST] Equation: $2\sqrt{1-x}-\sqrt{1+x}+\sqrt{1-x^2}=3-x$ $2\sqrt{1-x}-\sqrt{1+x}+\sqrt{1-x^2}=3-x$
Could someone help me solve this problem?
 [/INST] Assuming that we are restricted to only real square roots: 
Substitute $a = \sqrt{1-x}$ and $b = \sqrt{1+x}$ to get $2a-b+ab = 2+a^2$
Solving for $b$ gives us $b = a-1+\dfrac{1}{a-1}$. 
Since $b$ must be non-negative, $a-1$ must be positive. Then, by AM-GM, we get that $b \ge 2$. 
However, $b = \sqrt{1+x} \ge 2$ iff $x \ge 3$, which makes $\sqrt{1-x}$ imaginary. 
Hence, there are no real solutions. 
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