How many positive integer $y$ such that equation $$4(x-1)e^x=y(e^x+xy-2x^2-3)$$ has solution with $x\in(1,5)$
I try $e^x\leq x+1$ instead of the equation we have $g(x)= x^2(4y+2) -x(y^2+y)+2y-4=0$ but I can't check $f(x)$ with $x\in(1,5)$
After that I try with logarit but I can't fin the solution.
I try $g(x)=4(x-1)e^x-y(e^x+xy-2x^2-3)\Longrightarrow g'(x)=(4x-y)(e^x+y)$. That's enought if check the sign of $g'(x)$.
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