Question

find the solution set x^2e^x = 2xe^x

Answer 1

This is of the form \(a\cdot b=a \cdot c\).
The solution of this form is \(a=0 \vee b=c\).

You have: \(x^2e^x=2xe^x\), so you could rewrite it as
(because \(a=e^x,~ b=x^2,~ c=2x\)):

\(e^x=0\vee x^2=2x \)

So can you do the next step?

Answer 2

I'm a bit confused. exponential equations both sides must have the same base right?

Answer 3

Point is, it is not only an exponential equation, there are other factors in the equation.
What I explained is, you can split up into two separate, simpler equations:

\(e^x=0\)
\(x^2=2x\)

Answer 4

Now, because \(e^x >0\), for all values of x, we can forget this part!
So we only have to solve \(x^2=2x\), or \(x^2-2x=0\)

Answer 5

ok, but what this "V" means?

Answer 6

Sorry, it just means "or" :)

Answer 7

oh, right. thanks

Answer 8

YW!
Can you find the solution(s) of \(x^2-2x=0\)?

Answer 9

x(x-2)=0 {0,2} ?

Answer 10

Yup!

Answer 11

ok, thank you

Answer 12

Welcome!