Розділ 3. КВАДРАТНІ РІВНЯННЯ » 24.30 (3-4)

3) 1/4x4 + x3 – 5/4x2 = 1/4x2(x2 + 4x – 5). x2 + 4x – 5 = 0; D = 16 + 4 • 5 = 36; x1 = (-4+6 )/2 = 1; x2 = (-4-6)/2 = –5. 1/4x2(x2 + 4x – 5) = 1/4x2(x – 1)(x + 5). 4) –1/2x5 + 2x4 + 6x3 = –1/2x3(x2 – 4x – 12). x2 – 4x – 12 = 0; D = (–4)2 – 4 • (–12) = 64; x1 = (4+8)/2 = 6; x2 = (4-8)/2 = –2. –1/2x3(x2 – 4x – 12) = –1/2x3(x – 6)(x + 2).