3.Решите уравнения: a) (2x-3)² + (3-4x)(x+5)=82; 6)(x-1)(x+1)=2(x-5)² – x(x-3).

Решение:

• а) \((2x-3)^2 + (3-4x)(x+5) = 82\)
• \(4x^2 - 12x + 9 + 3x + 15 - 4x^2 - 20x = 82\)
• \(-29x + 24 = 82\)
• \(-29x = 58\)
• \(x = -2\)
• б) \((x-1)(x+1) = 2(x-5)^2 - x(x-3)\)
• \(x^2 - 1 = 2(x^2 - 10x + 25) - x^2 + 3x\)
• \(x^2 - 1 = 2x^2 - 20x + 50 - x^2 + 3x\)
• \(x^2 - 1 = x^2 - 17x + 50\)
• \(17x = 51\)
• \(x = 3\)