Question

(1-у)³+8у= 7+у²(3-у) Помогите решить уравнение..

Answer 1

По формуле раскрываем (1-у)^3 и вторые скобки с y^2

Получим:

1-3у+3у^2-y^3+8y=7+3y^2-Y^3

Убираем равное с обоих сторон(ну как бы перенесем с обратным знаком и вычислим)

1-3y+8y=7

Приведем подобные

1+5y=7

Перенесем 1 вправо с другим знаком

5у=7-1

5у=6

Разделим обе стороны на 5

у=6/5

Это и будет ответ, правильно будет записать 1(1/5)(одна целая одна пятая)

Answer 2

Solving the Equation (1-у)³ + 8у = 7 + у²(3-у)

To solve the equation (1-у)³ + 8у = 7 + у²(3-у), we'll start by expanding and simplifying the terms to isolate the variable 'у'.

First, let's expand the cubic term (1-у)³ using the formula (a-b)³ = a³ - 3a²b + 3ab² - b³.

Expanding (1-у)³: (1-у)³ = 1³ - 3 * 1² * у + 3 * 1 * у² - у³ = 1 - 3у + 3у² - у³

Now, we can substitute this expansion into the original equation and continue simplifying.

Expanding the original equation: (1-у)³ + 8у = 7 + у²(3-у) (1 - 3у + 3у² - у³) + 8у = 7 + 3у² - у³

Simplify the equation: 1 - 3у + 3у² - у³ + 8у = 7 + 3у² - у³ 1 - 3у + 3у² - у³ + 8у = 7 + 3у² - у³

Combine like terms: 1 + 8у - 3у + 3у² - у³ = 7 + 3у² - у³

Rearranging the terms: 3у² - у³ + 8у - 3у + 1 = 7 + 3у² - у³

Simplify further: 3у² - у³ + 5у + 1 = 7

Subtract 7 from both sides: 3у² - у³ + 5у + 1 - 7 = 0 3у² - у³ + 5у - 6 = 0

Now, the equation has been simplified to 3у² - у³ + 5у - 6 = 0. This is the simplified form of the given equation.

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