<s>[INST] Let a function $f(x)= \sqrt{(x^2-2x+2)(-x^2+3x+10)}-\sqrt{(-x^{2}+x-1)(x^{2}+x-6)}$ Let a function $f(x)= \sqrt{(x^2-2x+2)(-x^2+3x+10)}-\sqrt{(-x^{2}+x-1)(x^{2}+x-6)}$ and its domain is $D=[a,b+c]$. What's the value of $a^3+b^3+c^3 \over abc$ ?
Any ideas ?
The answer is $\boxed{3}$ .
 [/INST] in the first term $x^2-2x+2$ is always greater than $0$. hence $-x^2+3x+10$ should be greater than or equal to $0$.
similarly for the second term $-x^2+x-1$ is always less than $0$. hence $x^2+x-6$ should be less than or equal to $0$. 
now find the common interval in which both inequality satisfies . the domain will be $[-2,2]$.
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