What are the solutions to the equation n^3=2n ?

The solutions to the equation n^3=2n are n=0,n=-sqrt(2),n=sqrt(2)

Find the zeros of n^3=2n

The zeros of n^3=2n are n=0,n=-sqrt(2),n=sqrt(2)

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n^{3} = 2 n

n = 0, n = - 2, n = 2

Decimal Notation

n = 0, n = - 1.41421 \dots, n = 1.41421 \dots

Solution steps

n^{3} = 2 n

Move

2 n

to the left side

n^{3} - 2 n = 0

Factor

n^{3} - 2 n : n (n + 2) (n - 2)

n (n + 2) (n - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

n = 0 or n + 2 = 0 or n - 2 = 0

Solve

n + 2 = 0 : n = - 2

Solve

n - 2 = 0 : n = 2

The solutions are

n = 0, n = - 2, n = 2

x^{3} + 2 x = 400

11000 = 3000 (1 + x)^{5}

3 x^{3} - 2 x^{2} + x - 1 = 0

- x^{3} - 2 x^{2} - x = 0

x^{3} - x^{2} - 16 x - 20 = 0

What are the solutions to the equation n^3=2n ?
The solutions to the equation n^3=2n are n=0,n=-sqrt(2),n=sqrt(2)
Find the zeros of n^3=2n
The zeros of n^3=2n are n=0,n=-sqrt(2),n=sqrt(2)