Решите уравнение: 1/x-8 - 1/x-2 = 1/x-11 - 1/x-10 - вопрос №18121111104105203 от Aleks19102007 14.01.2021 02:14

Question

Алгебра: Решите уравнение: 1/x-8 - 1/x-2 = 1/x-11 - 1/x-10

Aleks19102007 · Answer

X - 2 - ( x - 8 ) / ( x - 8)( x - 2) = x - 10 - ( x - 11) / ( x - 11)( x - 10)
x - 2 - x + 8 / ( x - 8)( x - 2) = x - 10 - x + 11 / ( x - 11)( x - 10)
6 / ( x - 8 )( x - 2) = 1 / ( x - 11)(x - 10)
6 × (x - 11)( x - 10) = 1 × ( x - 8 )( x - 2)
6 × ( x² - 10x - 11x + 110) = x² - 2x - 8x + 16
6 × ( x² - 21x + 110) = x² - 10x + 16
6x² - 126x + 660 - x² + 10x - 16 = 0
5x² - 116x + 644 = 0
D = b² - 4ac = ( - 116)² - 4 × 5 × 644 = 13456 - 20 × 644 = 13456 - 12880 = 576 = 24²
x₁ = 116 + 24 / 10 = 14
x₂ = 116 - 24 / 10 = 9,2