What are the solutions to the equation x^5=(2-x)^3 ?

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

Find the zeros of x^5=(2-x)^3

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

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x^{5} = (2 - x)^{3}

x = 1

Solution steps

x^{5} = (2 - x)^{3}

Expand

(2 - x)^{3} : 8 - 12 x + 6 x^{2} - x^{3}

x^{5} = 8 - 12 x + 6 x^{2} - x^{3}

Subtract

8 - 12 x + 6 x^{2} - x^{3}

from both sides

x^{5} - (8 - 12 x + 6 x^{2} - x^{3}) = 8 - 12 x + 6 x^{2} - x^{3} - (8 - 12 x + 6 x^{2} - x^{3})

Simplify

x^{5} + x^{3} - 6 x^{2} + 12 x - 8 = 0

Factor

x^{5} + x^{3} - 6 x^{2} + 12 x - 8 : (x - 1) (x^{4} + x^{3} + 2 x^{2} - 4 x + 8)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{4} + x^{3} + 2 x^{2} - 4 x + 8 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{4} + x^{3} + 2 x^{2} - 4 x + 8 = 0 :

No Solution for

x \in R

The solution is

x = 1

5 x^{4} = 3, x^{2} = 8

2 x^{5} - 6 x^{3} + 8 x^{2} - 5 = 0

(x^{3} - 4 x^{2}) = (16 x - 64)

15 x^{4} + 15 x^{2} = 0

- x^{3} + 10 x^{2} - 31 x + 30 = 0

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