What are the solutions to the equation (x+1)^4+(x+5)^4=32 ?

The solutions to the equation (x+1)^4+(x+5)^4=32 are x=-3,x=-3+2sqrt(6)i,x=-3-2sqrt(6)i

Find the zeros of (x+1)^4+(x+5)^4=32

The zeros of (x+1)^4+(x+5)^4=32 are x=-3,x=-3+2sqrt(6)i,x=-3-2sqrt(6)i

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(x + 1)^{4} + (x + 5)^{4} = 32

x = - 3, x = - 3 + 26 i, x = - 3 - 26 i

Solution steps

(x + 1)^{4} + (x + 5)^{4} = 32

Expand

(x + 1)^{4} + (x + 5)^{4} : 2 x^{4} + 24 x^{3} + 156 x^{2} + 504 x + 626

2 x^{4} + 24 x^{3} + 156 x^{2} + 504 x + 626 = 32

Move

32

to the left side

2 x^{4} + 24 x^{3} + 156 x^{2} + 504 x + 594 = 0

Factor

2 x^{4} + 24 x^{3} + 156 x^{2} + 504 x + 594 : 2 (x + 3)^{2} (x^{2} + 6 x + 33)

2 (x + 3)^{2} (x^{2} + 6 x + 33) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x^{2} + 6 x + 33 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x^{2} + 6 x + 33 = 0 : x = - 3 + 26 i, x = - 3 - 26 i

The solutions are

x = - 3, x = - 3 + 26 i, x = - 3 - 26 i

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

z^{3} + 1 = 0

4 x^{4} + 2 x^{2} - 24 = 0

m^{3} - 6 m^{2} + 11 m - 6 = 0

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

What are the solutions to the equation (x+1)^4+(x+5)^4=32 ?
The solutions to the equation (x+1)^4+(x+5)^4=32 are x=-3,x=-3+2sqrt(6)i,x=-3-2sqrt(6)i
Find the zeros of (x+1)^4+(x+5)^4=32
The zeros of (x+1)^4+(x+5)^4=32 are x=-3,x=-3+2sqrt(6)i,x=-3-2sqrt(6)i