√10-x^2-2x+1=0 Корень из 10x-x^2 минус 2х+1=0

Question

√10-x^2-2x+1=0
Корень из 10x-x^2 минус 2х+1=0

Answer 1

√10x - x² - 2x + 1 = 0
√10x - x² = 2x - 1
10x - x² = (2x - 1)²
10x - x² = (2x - 1)(2x - 1)
10x - x² = 4x² - 2x - 2x + 1
10x - x² = 4x² - 4x + 1
10x - x² - 4x² + 4x - 1 = 0
- 5x² + 14x - 1 = 0
5x² - 14x + 1 = 0
D = b² - 4ac
D = (-14)² - 4 × 5 × 1 = 196 - 20 = 176
x₁ = 14 + √176/ 10, x₂ = 14 - √176/ 10