Решите уравнение:
а) (x²-2)/2 - 11x = 11;     б) (x²+x)/2; = (8x-7)/3
в) (4x²-1)/3 = x(10x - 9); г) 3/4x² - 2/5x = 4/5x² + 3/4.

Решение:


а) (x²-2)/2 - 11x = 11; x² - 1 - 22x = 22; x² - 22x - 23 = 0; D₁ = 121 + 23 = 144; x = 11 ± 12; x₁ = 23; x₂ = -1;
б) (x²+x)/2; = (8x-7)/3; 3x² + 3x = 16х - 14; 3x² - 13x + 14 = 0; D = 169 - 4 •3 • 14 = 169 - 168 = 1; x = (13±1)/6;
x₁ = 2; x₂ = 2 1/3;
в) (4x²-1)/3 = x(10x - 9); 4x² - 1 = 30x² - 27x; 26x² - 27x + 1; D = 27² - 4 • 26 = 729 - 104 = 625; x = (27±25)/52;
x₁ = 1/26; x₂ = 1;
г) 3/4x² - 2/5x = 4/5x² + 3/4; 15x² - 8x = 16x² + 15; x² + 8x + 15 = 0; D₁ = 16 - 15 = 1; x = -4 ± 1; x₁ = -5; x₂ = -3.