What is the answer to 3x^2ln(x)+x^2=0 ?

The answer to 3x^2ln(x)+x^2=0 is x= 1/(\sqrt[3]{e)}

Solve for x: 3x^2ln(x)+x^2=0

The solution is x= 1/(\sqrt[3]{e)}

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3 x^{2} ln (x) + x^{2} = 0

x = \frac{1}{3 e}

Decimal

x = 0.71653 \dots

Solution steps

3 x^{2} ln (x) + x^{2} = 0

Move

x^{2}

to the right side

3 x^{2} ln (x) = - x^{2}

Move

x^{2}

to the left side

3 x^{2} ln (x) + x^{2} = 0

Factor

3 x^{2} ln (x) + x^{2} : x^{2} (3 ln (x) + 1)

x^{2} (3 ln (x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 ln (x) + 1 = 0

Solve

3 ln (x) + 1 = 0 : x = \frac{1}{3 e}

Verify Solutions:

x = 0

False

, x = \frac{1}{3 e}

True

The solution is

x = \frac{1}{3 e}

lo g_{3} (x) + 1 = 0

lo g_{3} (2 x) - lo g_{3} (x + 5) = 0

2 ln (x) - ln (3) = 0

1 + lo g_{3} (x + 1) = 0

2 x \times ln (x) + x = 0

What is the answer to 3x^2ln(x)+x^2=0 ?
The answer to 3x^2ln(x)+x^2=0 is x= 1/(\sqrt[3]{e)}
Solve for x: 3x^2ln(x)+x^2=0
The solution is x= 1/(\sqrt[3]{e)}