Question

(y-3)^3+2y(5y+1)=y3-(2y-1)^2-26

Answer 1

Раскрываем скобки, приводим подобные и получаем квадратное уравнение:

$(y - 3)^3 + 2y(5y + 1) = y^3 - (2y - 1)^2 - 26\\ y^3-9y^2+27y-27+10y^2+2y=y^3-4y^2+4y-1-26\\5y^2+25y=0\\y^2+5y=0\\\left[\begin{array}{c}y=0\\y=-5\end{array}\right.$

Answer 2

Решение на фотографии

Answer 3

To solve the equation, let's simplify both sides step by step:

Given equation: (y-3)^3 + 2y(5y+1) = y^3 - (2y-1)^2 - 26

Step 1: Expand the expressions

Expanding the left side: (y-3)^3 = (y-3)(y-3)(y-3) = (y^2 - 6y + 9)(y-3) = y^3 - 9y^2 + 27y - 27

Expanding the term 2y(5y+1): 2y(5y+1) = 10y^2 + 2y

Expanding the right side: (2y-1)^2 = (2y-1)(2y-1) = 4y^2 - 4y + 1

Step 2: Rewrite the equation with the simplified expressions

The given equation becomes: (y^3 - 9y^2 + 27y - 27) + (10y^2 + 2y) = y^3 - (4y^2 - 4y + 1) - 26

Step 3: Group like terms on both sides

Combining like terms on the left side: y^3 - 9y^2 + 27y - 27 + 10y^2 + 2y = y^3 + 2y^2 + 29y - 27

Step 4: Simplify the equation

Now, the equation becomes: y^3 + 2y^2 + 29y - 27 = y^3 - (4y^2 - 4y + 1) - 26

Step 5: Eliminate y^3 terms by subtracting y^3 from both sides

y^3 - y^3 + 2y^2 + 29y - 27 = -4y^2 + 4y - 1 - 26

Step 6: Simplify further

2y^2 + 29y - 27 = -4y^2 + 4y - 27

Step 7: Move all terms to one side to solve for y

2y^2 + 29y - 27 + 4y^2 - 4y + 27 = 0

Step 8: Combine like terms

6y^2 + 25y = 0

Step 9: Factor out common terms

y(6y + 25) = 0

Step 10: Find the values of y

Now, set each factor to zero and solve for y:

1. y = 0
2. 6y + 25 = 0 6y = -25 y = -25/6

So the solutions to the equation are y = 0 and y = -25/6.