<s>[INST] Solve $x+y-2=0$ and $y= x^3$ for $x$ and $y$ This is not a full question but needs to be solved to evaluate area using double integral. I need to solve 
$$x+y=2$$ 
$$y=x^3$$
If I put $y= x^3$ in first equation I get messy $x+ x^3 -2=0$ to solve to find what $x$ is? How to do it using viable methods from calculus, or any other quick way.
 [/INST] Clearly, $x=1$ satisfies $x^3+x-2=0$
Alternatively, $x^3+x-2=x^3-1+x-1=(x-1)(x^2+x+1)+(x-1)=\cdots$ 
the rest $\dfrac{x^3+x-2}{x-1}=0$ is a Quadratic equation, right?
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