What are the solutions to the equation (2x-1)^5=x^5 ?

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

Find the zeros of (2x-1)^5=x^5

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

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

x = 1

Solution steps

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

Expand

(2 x - 1)^{5} : 32 x^{5} - 80 x^{4} + 80 x^{3} - 40 x^{2} + 10 x - 1

32 x^{5} - 80 x^{4} + 80 x^{3} - 40 x^{2} + 10 x - 1 = x^{5}

Move

x^{5}

to the left side

31 x^{5} - 80 x^{4} + 80 x^{3} - 40 x^{2} + 10 x - 1 = 0

Factor

31 x^{5} - 80 x^{4} + 80 x^{3} - 40 x^{2} + 10 x - 1 : (x - 1) (31 x^{4} - 49 x^{3} + 31 x^{2} - 9 x + 1)

(x - 1) (31 x^{4} - 49 x^{3} + 31 x^{2} - 9 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or 31 x^{4} - 49 x^{3} + 31 x^{2} - 9 x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

31 x^{4} - 49 x^{3} + 31 x^{2} - 9 x + 1 = 0 :

No Solution for

x \in R

The solution is

x = 1

x^{3} - 12 x^{2} + 60 x - 128 = 0

(x + 3)^{3} = 729

4 x^{3} - 11 x^{2} + 2 x + 3 = 0

I, 50 = π^{2} E I^{7}

z^{4} - 6 z^{2} + 25 = 0

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