What are the solutions to the equation (x-4)^4=x^4 ?

The solutions to the equation (x-4)^4=x^4 are x=2,x=2+2i,x=2-2i

Find the zeros of (x-4)^4=x^4

The zeros of (x-4)^4=x^4 are x=2,x=2+2i,x=2-2i

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(x - 4)^{4} = x^{4}

x = 2, x = 2 + 2 i, x = 2 - 2 i

Solution steps

(x - 4)^{4} = x^{4}

Expand

(x - 4)^{4} : x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256

x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256 = x^{4}

Move

x^{4}

to the left side

- 16 x^{3} + 96 x^{2} - 256 x + 256 = 0

Factor

- 16 x^{3} + 96 x^{2} - 256 x + 256 : - 16 (x - 2) (x^{2} - 4 x + 8)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

x = 2, x = 2 + 2 i, x = 2 - 2 i

2.5 x^{4} + 3 x^{3} - 2.6 x^{2} - 5.1 x - 5.6 = 0

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

x^{6} - 2 = 0

x^{3} - 11 x^{2} + 43 x - 65

x^{4} + 9 x^{3} + 19 x^{2} - 18 x - 56 = 0

What are the solutions to the equation (x-4)^4=x^4 ?
The solutions to the equation (x-4)^4=x^4 are x=2,x=2+2i,x=2-2i
Find the zeros of (x-4)^4=x^4
The zeros of (x-4)^4=x^4 are x=2,x=2+2i,x=2-2i