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.
