Решите уравнения: 1. 2x^2 − 4√2x + 3 = 0 2. x^2 − x(√7−2) − 2√7 = 0 3. 2x^2 − 4x − 17 = 0

Question

Решите уравнения: 1. 2x^2 − 4√2x + 3 = 0 2. x^2 − x(√7−2) − 2√7 = 0 3. 2x^2 − 4x − 17 = 0

Answer 1

2x^3 - 11x^2 + 17x - 6 = 2x^3 - 4x^2 - 7x^2 + 14x + 3x - 6 =  

= 2x^2 * (x - 2) - 7x * (x - 2) + 3 * (x - 2) =  

= (x - 2) * (2x^2 - 7x + 3) = (x - 2) * (x - 3) * (2x - 1) = 0  

x1 = 2  

x2 = 3  

x3 = 0,5  

Среднее арифметическое = (2 + 3 + 0,5) / 3 = 11/6