What are the solutions to the equation (x-2)^6+(x-4)^6=64 ?

The solutions to the equation (x-2)^6+(x-4)^6=64 are x=2,x=4

Find the zeros of (x-2)^6+(x-4)^6=64

The zeros of (x-2)^6+(x-4)^6=64 are x=2,x=4

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(x - 2)^{6} + (x - 4)^{6} = 64

x = 2, x = 4

Solution steps

(x - 2)^{6} + (x - 4)^{6} = 64

Expand

(x - 2)^{6} + (x - 4)^{6} : 2 x^{6} - 36 x^{5} + 300 x^{4} - 1440 x^{3} + 4080 x^{2} - 6336 x + 4160

2 x^{6} - 36 x^{5} + 300 x^{4} - 1440 x^{3} + 4080 x^{2} - 6336 x + 4160 = 64

Move

64

to the left side

2 x^{6} - 36 x^{5} + 300 x^{4} - 1440 x^{3} + 4080 x^{2} - 6336 x + 4096 = 0

Factor

2 x^{6} - 36 x^{5} + 300 x^{4} - 1440 x^{3} + 4080 x^{2} - 6336 x + 4096 : 2 (x - 2) (x - 4) (x^{4} - 12 x^{3} + 70 x^{2} - 204 x + 256)

2 (x - 2) (x - 4) (x^{4} - 12 x^{3} + 70 x^{2} - 204 x + 256) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x - 4 = 0 or x^{4} - 12 x^{3} + 70 x^{2} - 204 x + 256 = 0

Solve

x - 2 = 0 : x = 2

Solve

x - 4 = 0 : x = 4

Solve

x^{4} - 12 x^{3} + 70 x^{2} - 204 x + 256 = 0 :

No Solution for

x \in R

The solutions are

x = 2, x = 4

x, f (x)^{4} + f (- x)^{4} = x^{2000}

2 a^{3} - 3 a^{2} + 2 a + 1 = 0

2 x^{5} - 5 x^{4} + 10 x + 3 = 0

1 x^{3} - 7 x + 6 = 0

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

What are the solutions to the equation (x-2)^6+(x-4)^6=64 ?
The solutions to the equation (x-2)^6+(x-4)^6=64 are x=2,x=4
Find the zeros of (x-2)^6+(x-4)^6=64
The zeros of (x-2)^6+(x-4)^6=64 are x=2,x=4