What is the answer to e^{-x}(x^2-5x+2)=0 ?

The answer to e^{-x}(x^2-5x+2)=0 is x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2

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e^{-x}(x^2-5x+2)=0

e^{- x} (x^{2} - 5 x + 2) = 0

x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

Decimal Notation

x = 4.56155 \dots, x = 0.43844 \dots

Solution steps

e^{- x} (x^{2} - 5 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x} = 0 or x^{2} - 5 x + 2 = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

x^{2} - 5 x + 2 = 0 : x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

y, 2^{x + y} = x

2 5^{x - 3} = (\frac{1}{125})^{x + 2}

(5^{x})^{2} - 26 (5^{x}) + 25 = 0

5^{x^{2} + x} = 1

2^{2 x + 2} + 3 = 2^{x + 3}

What is the answer to e^{-x}(x^2-5x+2)=0 ?
The answer to e^{-x}(x^2-5x+2)=0 is x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2