What are the solutions to the equation (x-6)^4+(x-8)^4=16 ?

The solutions to the equation (x-6)^4+(x-8)^4=16 are x=6,x=8,x=7+sqrt(7)i,x=7-sqrt(7)i

Find the zeros of (x-6)^4+(x-8)^4=16

The zeros of (x-6)^4+(x-8)^4=16 are x=6,x=8,x=7+sqrt(7)i,x=7-sqrt(7)i

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(x - 6)^{4} + (x - 8)^{4} = 16

x = 6, x = 8, x = 7 + 7 i, x = 7 - 7 i

Solution steps

(x - 6)^{4} + (x - 8)^{4} = 16

Expand

(x - 6)^{4} + (x - 8)^{4} : 2 x^{4} - 56 x^{3} + 600 x^{2} - 2912 x + 5392

2 x^{4} - 56 x^{3} + 600 x^{2} - 2912 x + 5392 = 16

Move

16

to the left side

2 x^{4} - 56 x^{3} + 600 x^{2} - 2912 x + 5376 = 0

Factor

2 x^{4} - 56 x^{3} + 600 x^{2} - 2912 x + 5376 : 2 (x - 6) (x - 8) (x^{2} - 14 x + 56)

2 (x - 6) (x - 8) (x^{2} - 14 x + 56) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 6 = 0 or x - 8 = 0 or x^{2} - 14 x + 56 = 0

Solve

x - 6 = 0 : x = 6

Solve

x - 8 = 0 : x = 8

Solve

x^{2} - 14 x + 56 = 0 : x = 7 + 7 i, x = 7 - 7 i

The solutions are

x = 6, x = 8, x = 7 + 7 i, x = 7 - 7 i

x^{3} - 6 x^{2} + 3 x + 9 = 0

9 x^{4} - 1 = 0

4 x^{4} - 4 x^{3} - 7 x^{2} - 4 x + 4 = 0

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

x, 2 (x^{4} - y^{4}) = 350

What are the solutions to the equation (x-6)^4+(x-8)^4=16 ?
The solutions to the equation (x-6)^4+(x-8)^4=16 are x=6,x=8,x=7+sqrt(7)i,x=7-sqrt(7)i
Find the zeros of (x-6)^4+(x-8)^4=16
The zeros of (x-6)^4+(x-8)^4=16 are x=6,x=8,x=7+sqrt(7)i,x=7-sqrt(7)i