What is the answer to 4x^2e^{-x^2}-2e^{-x^2}=0 ?

The answer to 4x^2e^{-x^2}-2e^{-x^2}=0 is x=-1/(sqrt(2)),x= 1/(sqrt(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4x^2e^{-x^2}-2e^{-x^2}=0

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

x = - \frac{1}{2}, x = \frac{1}{2}

Decimal Notation

x = - 0.70710 \dots, x = 0.70710 \dots

Solution steps

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

Factor

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

2 e^{- x^{2}} (2 x + 1) (2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x^{2}} = 0 or 2 x + 1 = 0 or 2 x - 1 = 0

Solve

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

No Solution for

x \in R

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

Solve

2 x - 1 = 0 : x = \frac{1}{2}

x = - \frac{1}{2}, x = \frac{1}{2}

\frac{1}{1 - e ^{x}} = 5

16 \cdot 1 0^{5 x} = 96

5^{x + 1} = 7

5^{x} - 0. 2^{x} = 4.8

2 e^{2 x} = 97

What is the answer to 4x^2e^{-x^2}-2e^{-x^2}=0 ?
The answer to 4x^2e^{-x^2}-2e^{-x^2}=0 is x=-1/(sqrt(2)),x= 1/(sqrt(2))