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Popular >

x^2e^{-x}=xe^{-x}

Solution

x^{2} e^{- x} = x e^{- x}

Solution

x = 0, x = 1

Solution steps

x^{2} e^{- x} = x e^{- x}

Subtract

x e^{- x}

from both sides

x^{2} e^{- x} - x e^{- x} = x e^{- x} - x e^{- x}

Simplify

x^{2} e^{- x} - x e^{- x} = 0

Factor

x^{2} e^{- x} - x e^{- x} : e^{- x} x (x - 1)

e^{- x} x (x - 1) = 0

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

e^{- x} = 0 or x = 0 or x - 1 = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

x - 1 = 0 : x = 1

x = 0, x = 1

Popular Examples

7^{2-x}-49^{2-x}+42=0

7^{2 - x} - 4 9^{2 - x} + 42 = 0

- \frac{1}{81} = - 3^{x}

9^{-x+5}=27^{6x-10}

9^{- x + 5} = 2 7^{6 x - 10}

e^{x + 2} = 5

e^{x + 2} = 8

Frequently Asked Questions (FAQ)

What is the answer to x^2e^{-x}=xe^{-x} ?
The answer to x^2e^{-x}=xe^{-x} is x=0,x=1