Question

(1+у )³ + (1 - у )³ -6у ² = 3у - 1

Answer 1

Решение на фото будут вопросы пишите

Answer 2

To solve the equation (1 + у)³ + (1 - у)³ - 6у² = 3у - 1, we'll first expand the cubes and then simplify the equation step by step:

Step 1: Expand the cubes (1 + у)³ = (1 + у)(1 + у)(1 + у) = (1 + у)(1 + 2у + у²) = 1 + 3у + 3у² + у³ (1 - у)³ = (1 - у)(1 - у)(1 - у) = (1 - у)(1 - 2у + у²) = 1 - 3у + 3у² - у³

Step 2: Substitute the expanded cubes into the equation (1 + у)³ + (1 - у)³ - 6у² = (1 + 3у + 3у² + у³) + (1 - 3у + 3у² - у³) - 6у² Simplify: 1 + 3у + 3у² + у³ + 1 - 3у + 3у² - у³ - 6у²

Step 3: Combine like terms (1 + 1) + (3у - 3у) + (3у² - 6у²) + (у³ - у³) Simplify: 2 + 0 - 3у² + 0

Step 4: Final equation 2 - 3у² = 3у - 1

Step 5: Move all terms to one side of the equation 2 - 3у² - 3у + 1 = 0

Step 6: Combine constants 3 - 3у² - 3у = 0

Step 7: Factor out common terms 3(1 - у² - у) = 0

Step 8: Set each factor to zero and solve for у 1 - у² - у = 0

Now, this is a quadratic equation in terms of у, so we can solve it using the quadratic formula: у = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = -1, and c = -1 у = (1 ± √((-1)² - 41(-1))) / 2*1 у = (1 ± √(1 + 4)) / 2 у = (1 ± √5) / 2

So the two solutions for у are:

1. у = (1 + √5) / 2
2. у = (1 - √5) / 2