What are the solutions to the equation (x+3)^4+(x+5)^4=16 ?

The solutions to the equation (x+3)^4+(x+5)^4=16 are x=-3,x=-5,x=-4+sqrt(7)i,x=-4-sqrt(7)i

Find the zeros of (x+3)^4+(x+5)^4=16

The zeros of (x+3)^4+(x+5)^4=16 are x=-3,x=-5,x=-4+sqrt(7)i,x=-4-sqrt(7)i

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(x + 3)^{4} + (x + 5)^{4} = 16

x = - 3, x = - 5, x = - 4 + 7 i, x = - 4 - 7 i

Solution steps

(x + 3)^{4} + (x + 5)^{4} = 16

Expand

(x + 3)^{4} + (x + 5)^{4} : 2 x^{4} + 32 x^{3} + 204 x^{2} + 608 x + 706

2 x^{4} + 32 x^{3} + 204 x^{2} + 608 x + 706 = 16

Move

16

to the left side

2 x^{4} + 32 x^{3} + 204 x^{2} + 608 x + 690 = 0

Factor

2 x^{4} + 32 x^{3} + 204 x^{2} + 608 x + 690 : 2 (x + 3) (x + 5) (x^{2} + 8 x + 23)

2 (x + 3) (x + 5) (x^{2} + 8 x + 23) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x + 5 = 0 or x^{2} + 8 x + 23 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x + 5 = 0 : x = - 5

Solve

x^{2} + 8 x + 23 = 0 : x = - 4 + 7 i, x = - 4 - 7 i

The solutions are

x = - 3, x = - 5, x = - 4 + 7 i, x = - 4 - 7 i

3 x^{3} - 8 x^{2} + 8 = 5 x + 5

(m^{4} + 25 m^{2} + 25) - 12 m^{2} - 60 m - 49 = 0

x^{4} + 2 x^{3} - 8 x - 16 = 0

(3 x - 4)^{10} - 3 = 1021

(3 x^{4})^{5} = (3^{3})^{3}

What are the solutions to the equation (x+3)^4+(x+5)^4=16 ?
The solutions to the equation (x+3)^4+(x+5)^4=16 are x=-3,x=-5,x=-4+sqrt(7)i,x=-4-sqrt(7)i
Find the zeros of (x+3)^4+(x+5)^4=16
The zeros of (x+3)^4+(x+5)^4=16 are x=-3,x=-5,x=-4+sqrt(7)i,x=-4-sqrt(7)i