What are the solutions to the equation y^3+81=36y ?

The solutions to the equation y^3+81=36y are y=3,y=(-3+3sqrt(13))/2 ,y=(-3-3sqrt(13))/2

Find the zeros of y^3+81=36y

The zeros of y^3+81=36y are y=3,y=(-3+3sqrt(13))/2 ,y=(-3-3sqrt(13))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{3} + 81 = 36 y

y = 3, y = \frac{- 3 + 3 13}{2}, y = \frac{- 3 - 3 13}{2}

Decimal Notation

y = 3, y = 3.90832 \dots, y = - 6.90832 \dots

Solution steps

y^{3} + 81 = 36 y

Move

36 y

to the left side

y^{3} + 81 - 36 y = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

y^{3} - 36 y + 81 = 0

Factor

y^{3} - 36 y + 81 : (y - 3) (y^{2} + 3 y - 27)

(y - 3) (y^{2} + 3 y - 27) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y - 3 = 0 or y^{2} + 3 y - 27 = 0

Solve

y - 3 = 0 : y = 3

Solve

y^{2} + 3 y - 27 = 0 : y = \frac{- 3 + 3 13}{2}, y = \frac{- 3 - 3 13}{2}

The solutions are

y = 3, y = \frac{- 3 + 3 13}{2}, y = \frac{- 3 - 3 13}{2}

x^{3} = 6

2 x^{3} - 5 x^{2} - 10 x + 3 = 0

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

x^{4} = 2

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

What are the solutions to the equation y^3+81=36y ?
The solutions to the equation y^3+81=36y are y=3,y=(-3+3sqrt(13))/2 ,y=(-3-3sqrt(13))/2
Find the zeros of y^3+81=36y
The zeros of y^3+81=36y are y=3,y=(-3+3sqrt(13))/2 ,y=(-3-3sqrt(13))/2