What are the solutions to the equation (x-5)^3-x+5=0 ?

The solutions to the equation (x-5)^3-x+5=0 are x=4,x=5,x=6

Find the zeros of (x-5)^3-x+5=0

The zeros of (x-5)^3-x+5=0 are x=4,x=5,x=6

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(x - 5)^{3} - x + 5 = 0

x = 4, x = 5, x = 6

Solution steps

(x - 5)^{3} - x + 5 = 0

Expand

(x - 5)^{3} - x + 5 : x^{3} - 15 x^{2} + 74 x - 120

x^{3} - 15 x^{2} + 74 x - 120 = 0

Factor

x^{3} - 15 x^{2} + 74 x - 120 : (x - 4) (x - 5) (x - 6)

(x - 4) (x - 5) (x - 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x - 5 = 0 or x - 6 = 0

Solve

x - 4 = 0 : x = 4

Solve

x - 5 = 0 : x = 5

Solve

x - 6 = 0 : x = 6

The solutions are

x = 4, x = 5, x = 6

(x^{3} + 1)^{3} = 8 (2 x - 1)

2 x^{3} + 5 x^{2} - 25 x = 0

A = (x + 1) (x - 1) (x^{2} + 1) + 1

c^{3} + 9 = 10

x^{4} + 4 x^{2} - 60 = 0

What are the solutions to the equation (x-5)^3-x+5=0 ?
The solutions to the equation (x-5)^3-x+5=0 are x=4,x=5,x=6
Find the zeros of (x-5)^3-x+5=0
The zeros of (x-5)^3-x+5=0 are x=4,x=5,x=6