Find the dependence n (a) the number of solutions the equation given a parameter
1) $x^3-3x=a$
2) $e^2x=ax$
3) $x^ax=e (x>0)$
For example what I did for (1) is
$x(x^2-3)=a$
$x=a , x^2-3=a$
$x^2 = a+3$
And thats it. I dont know how to continue from here.
I need some hints please.
thanks!
I think I understood the situation, you need to draw the graph function and see if for example y = a ie a = 4,3,2,1, or any other number, how many times he cuts the graph of the function, eg a> 0 then there are two solutions (ie twice cut the graph).