What are the solutions to the equation x^3-24x+32=0 ?

The solutions to the equation x^3-24x+32=0 are x=4,x=2(sqrt(3)-1),x=-2(1+sqrt(3))

Find the zeros of x^3-24x+32=0

The zeros of x^3-24x+32=0 are x=4,x=2(sqrt(3)-1),x=-2(1+sqrt(3))

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x^{3} - 24 x + 32 = 0

x = 4, x = 2 (3 - 1), x = - 2 (1 + 3)

Decimal Notation

x = 4, x = 1.46410 \dots, x = - 5.46410 \dots

Solution steps

x^{3} - 24 x + 32 = 0

Factor

x^{3} - 24 x + 32 : (x - 4) (x^{2} + 4 x - 8)

(x - 4) (x^{2} + 4 x - 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{2} + 4 x - 8 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{2} + 4 x - 8 = 0 : x = 2 (3 - 1), x = - 2 (1 + 3)

The solutions are

x = 4, x = 2 (3 - 1), x = - 2 (1 + 3)

x (x^{2} + 3) = 8

y^{3} + y^{2} = 49 y + 49

2 x^{3} = 10 x

2 x^{3} = 128

3 (4 g^{6}) = 2 (6 g^{9})

What are the solutions to the equation x^3-24x+32=0 ?
The solutions to the equation x^3-24x+32=0 are x=4,x=2(sqrt(3)-1),x=-2(1+sqrt(3))
Find the zeros of x^3-24x+32=0
The zeros of x^3-24x+32=0 are x=4,x=2(sqrt(3)-1),x=-2(1+sqrt(3))