What are the solutions to the equation (x-4)^2=(x-4)^4 ?

The solutions to the equation (x-4)^2=(x-4)^4 are x=3,x=4,x=5

Find the zeros of (x-4)^2=(x-4)^4

The zeros of (x-4)^2=(x-4)^4 are x=3,x=4,x=5

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(x - 4)^{2} = (x - 4)^{4}

x = 3, x = 4, x = 5

Solution steps

(x - 4)^{2} = (x - 4)^{4}

Expand

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

Expand

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

x^{2} - 8 x + 16 = x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256

Switch sides

x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256 = x^{2} - 8 x + 16

Move

16

to the left side

x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 240 = x^{2} - 8 x

Move

8 x

to the left side

x^{4} - 16 x^{3} + 96 x^{2} - 248 x + 240 = x^{2}

Move

x^{2}

to the left side

x^{4} - 16 x^{3} + 95 x^{2} - 248 x + 240 = 0

Factor

x^{4} - 16 x^{3} + 95 x^{2} - 248 x + 240 : (x - 3) (x - 4)^{2} (x - 5)

(x - 3) (x - 4)^{2} (x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x - 4 = 0 or x - 5 = 0

Solve

x - 3 = 0 : x = 3

Solve

x - 4 = 0 : x = 4

Solve

x - 5 = 0 : x = 5

The solutions are

x = 3, x = 4, x = 5

2 x^{3} + 5 x - 1 = 0

x^{3} - x - 20 = 0

8.62 x^{3} - 4.5833 x - 0.8035 = 0

15 x^{3} + 14 x^{2} - 8 x = 9

15 x^{3} + 14 x^{2} - 8 x = 0

What are the solutions to the equation (x-4)^2=(x-4)^4 ?
The solutions to the equation (x-4)^2=(x-4)^4 are x=3,x=4,x=5
Find the zeros of (x-4)^2=(x-4)^4
The zeros of (x-4)^2=(x-4)^4 are x=3,x=4,x=5