Вправи 888 - 1000 » 986

986. Розв’яжи рівняння. а) (2,5x – 7)(2x + 3) + Зx + 4 = (4x – 9)(1,5x + 1); 5x2 + 7,5x – 14x – 21 + Зx + 4 = 6x2 + 4x – 13,5x – 9; 5x2 + 7,5x – 14x – 21 + Зx + 4 – 6x2 – 4x + 13,5x + 9 = 0; –x2 + 6x – 8 = 0; x2 – 6x + 8 = 0; x = (3 ± √(9-8))/1 = (3 ±1)/1; x1 = 4; x2 = 2; б) (Зz – 5)(4z + 1) + (2z + 3)(5z – 4) = 6z(3 + 2z) – 11; 12z2 + Зz – 20z – 5 + 10z2 – 8z + 15z – 12 = 18z + 12z2 – 11; 22z2 – 10z – 17 – 18z – 12z2 + 11 = 0; 10z2 – 28z – 6 = 0; 5z2 – 14z – 3 = 0; z = (7 ± √(49+15))/5 = (7 ±8)/5; z1 = 3; z2 = –1/5. Відповідь: а) 4; 2; б) 3; –1/5. в) x2 + 2√2 + 1 = 0; x = –√2 ± √(2-1); x = –√2 ± 1; г) x2 – 3√2 + 4 = 0; x = (3√2 ± √(18-16))/2; x = (3√2 ± √2)/2; x1 = 2√2; x2 = √2. Відповідь: в) 1 – √2; – 1 – √2; г) 2√2; √2.