1дробь Х+2дробьХ+2=1

Question

1дробь Х+2дробьХ+2=1

Answer 1

1/x + 2/x + 2 = 1
1/x = 1 - 2/x + 2
1/x = (x + 2 - 2) / x + 2
1/x = x / x + 2
x × x = x + 2
x² = x + 2
x² - x - 2 = 0
D = b² - 4ac = ( - 1)² - 4 × 1 × ( - 2) = 1 + 8 = 9 = 3²
x₁ = 1 + 3 / 2 = 4 / 2 = 2
x₂ = 1 - 3 / 2 = - 2 / 2 = - 1