(3x+2)²+(4x-1)(4x+1)=(5x-1)²

Решение:

Given equation: (3x+2)² + (4x-1)(4x+1) = (5x-1)²

First, let's expand each side of the equation:

Expanding (3x+2)²: (3x+2)² = (3x+2)(3x+2) = 9x² + 6x + 6x + 4 = 9x² + 12x + 4

Expanding (4x-1)(4x+1): (4x-1)(4x+1) = 4x4x + 4x1 - 14x - 11 = 16x² + 4x - 4x - 1 = 16x² - 1

Expanding (5x-1)²: (5x-1)² = (5x-1)(5x-1) = 25x² - 5x - 5x + 1 = 25x² - 10x + 1

Now, substitute the expanded expressions back into the original equation:

(9x² + 12x + 4) + (16x² - 1) = (25x² - 10x + 1)

Combine like terms on both sides of the equation:

9x² + 12x + 4 + 16x² - 1 = 25x² - 10x + 1 25x² + 12x + 4 - 1 = 25x² - 10x + 1 25x² + 12x + 3 = 25x² - 10x + 1

Now, simplify the equation by bringing all terms to one side:

25x² - 25x² + 12x + 10x = 1 - 3 22x = -2 x = -2/22 x = -1/11

Therefore, the solution to the equation (3x+2)² + (4x-1)(4x+1) = (5x-1)² is x = -1/11.