Розділ 3. КВАДРАТНІ РІВНЯННЯ » 21.6

Розв’яжіть рівняння: 1) x2 – 5x + 6 = 0; D = (–5)2 – 4 • 1 • 6 =1; x1 = (5+ √1)/2 = (5+1)/2 = 3; x2 = (5- √1)/2 = (5-1)/2 = 2. 2) 2x2 + 5x – 3 = 0; D = (–5)2 – 4 • 2 • (–3) = 49; √D = 7; x1 = (-5+ 7)/(2 •2) = 2/4 = 0,5; x2 = (-5- 7)/(2 •2) = (-12)/4 = –3. 3) 3x2 + 5x + 2 = 0; D = 52 – 4 • 3 • 2 = 1; √D = 1; x1 = (-5+ 1)/(2 •3) = (-4)/6 = –2/3; x2 = (-5- 1)/6 = –1. 4) x2 + 10x + 25 = 0; D = 102 – 4 • 1 • 25 = 0; x = (-10)/2 = –5. 5) x2 + x – 90 = 0; D = 12 – 4 • 1 • (–90) = 361; √D = 19; x1 = (-1+ 19)/(2 ) = 18/2 = 9; x2 = (-1- 19)/(2 ) = (-20)/2 = –10. 6) x2 – 10x – 24 = 0; D = (–10)2 – 4 • 1 • (–24) = 100 + 96 = 196; √D = 14; x1 = (10+ 14)/(2 ) = 24/2 = 12; x2 = (10 - 14)/(2 ) = (-4)/2 = –2.