What are the solutions to the equation y^5+y^3+y=3 ?

The solutions to the equation y^5+y^3+y=3 are y=1

Find the zeros of y^5+y^3+y=3

The zeros of y^5+y^3+y=3 are y=1

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y^{5} + y^{3} + y = 3

y = 1

Solution steps

y^{5} + y^{3} + y = 3

Move

3

to the left side

y^{5} + y^{3} + y - 3 = 0

Factor

y^{5} + y^{3} + y - 3 : (y - 1) (y^{4} + y^{3} + 2 y^{2} + 2 y + 3)

(y - 1) (y^{4} + y^{3} + 2 y^{2} + 2 y + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y - 1 = 0 or y^{4} + y^{3} + 2 y^{2} + 2 y + 3 = 0

Solve

y - 1 = 0 : y = 1

Solve

y^{4} + y^{3} + 2 y^{2} + 2 y + 3 = 0 :

No Solution for

y \in R

The solution is

y = 1

- 3 = x^{6} - 8

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

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

x^{3} - x^{2} - x - 25 = 470

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

What are the solutions to the equation y^5+y^3+y=3 ?
The solutions to the equation y^5+y^3+y=3 are y=1
Find the zeros of y^5+y^3+y=3
The zeros of y^5+y^3+y=3 are y=1