x^3e^x - 4e^x =0
e^x (x^3 - 4) = 0
e^x = 0
x = -oo
x^3 = 4
x = 4^(.333....)
Not sure if you do complex arithmetic
360/3 = 120
if so you also have two complex roots
one at +120 degrees and one at - 120
x = r (cos 120 + i sin 120)
x = 4^(1/3) ( -.5 + i sqrt3/2)
x = 4^.3333...(.5)(-1+isqrt 3)
and the other is
x = 4^.3333...(.5)(-1-isqrt 3)
but the answers are 0,-2,2
If the equation is as you typed my money is riding with Damon.
Your answers don't even come close to satisfying the equation.
are u sure b/c the answers are from the book
To solve the equation x^3e^x - 4e^x = 0, we can rewrite it as a common factor:
e^x(x^3 - 4) = 0
Now, we have two possibilities for the equation to be true:
1. e^x = 0:
This is not possible since e^x is always positive. So, we can ignore this possibility.
2. x^3 - 4 = 0:
To find the values of x that satisfy this equation, we can solve for x:
x^3 = 4
Taking the cube root of both sides, we get:
x = ∛4
Now, we need to find the cube root of 4. We can approximate this using a calculator or a mathematical software. The exact value is ∛4 ≈ 1.5874.
Therefore, the solution for the equation x^3e^x - 4e^x = 0 is x ≈ 1.5874.