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

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

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

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

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

y = 1

Solution steps

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

Switch sides

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

9 x^{3} - 45 x^{2} - 52 x - 12 = 0

z^{6} + 64 = 0

y^{3} - 9 y - 12 = 0

x^{3} + 4 x^{2} = 5 x

x^{3} = 6 x^{2}

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