What are the solutions to the equation (x-1)^3=(x-1)^5 ?

The solutions to the equation (x-1)^3=(x-1)^5 are x=0,x=1,x=2

Find the zeros of (x-1)^3=(x-1)^5

The zeros of (x-1)^3=(x-1)^5 are x=0,x=1,x=2

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(x - 1)^{3} = (x - 1)^{5}

x = 0, x = 1, x = 2

Solution steps

(x - 1)^{3} = (x - 1)^{5}

Expand

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

Expand

(x - 1)^{5} : x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

x^{3} - 3 x^{2} + 3 x - 1 = x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

Switch sides

x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1 = x^{3} - 3 x^{2} + 3 x - 1

Move

1

to the right side

x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x = x^{3} - 3 x^{2} + 3 x

Subtract

x^{3} - 3 x^{2} + 3 x

from both sides

x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - (x^{3} - 3 x^{2} + 3 x) = x^{3} - 3 x^{2} + 3 x - (x^{3} - 3 x^{2} + 3 x)

Simplify

x^{5} - 5 x^{4} + 9 x^{3} - 7 x^{2} + 2 x = 0

Factor

x^{5} - 5 x^{4} + 9 x^{3} - 7 x^{2} + 2 x : x (x - 1)^{3} (x - 2)

x (x - 1)^{3} (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x - 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 2 = 0 : x = 2

The solutions are

x = 0, x = 1, x = 2

892.22488 m^{3} - 7994.754 m - 16974 = 0

(x) = 8 x^{6} + 10 x^{3} + 4 x^{2} + 4

b^{3} - b = 15

x^{3} - 23 x^{2} + 142 x - 12 = 0

(x) = (x^{2} + 7 x - 8)^{2}

What are the solutions to the equation (x-1)^3=(x-1)^5 ?
The solutions to the equation (x-1)^3=(x-1)^5 are x=0,x=1,x=2
Find the zeros of (x-1)^3=(x-1)^5
The zeros of (x-1)^3=(x-1)^5 are x=0,x=1,x=2