Корень из 1-2х+х^2 +корень из 26+3х-5х^2=х-1

Question

Корень из 1-2х+х^2 +корень из 26+3х-5х^2=х-1

Answer 1

1 - 2х + х² = 0
х² - 2х + 1 = 0; D = 4 - 2 = 2
x₁ = (2 - √2)/2 = 2/2 - √2/2 = 1 - 1/√2
x₂ = (2 + √2)/2 = 1 + 1/2

26 + 3x - 5x² = x - 1
26 + 3x - 5x² - x + 1 = 0
27 + 2x - 5x² = 0
-5x² + 2x + 27 = 0
D = 2² - 4 * (-5) * 27 = 4 + 540 = 544
√D = √16*34 = 4√34
x₁ = (-2 - 4√34) / -10 = -2(1 + 2√34) / -10 = (1 + 2√34) / 5
x₂ = (-2 + 4√34) / -10 = -2(1 - 2√34) / -10 = (1 - 2√34) / 5