Задача №698
Найдите корень уравнения:
а) 5 + х2 = (х + 1)(x + 6);
б) 2х(х - 8) = (х + 1)(2x - 3);
в) (3x - 2)(х + 4) - 3(х + 5)(х - 1) = 0;
г) х2 + х(6 - 2х) = (х- 1)(2 - х) - 2.
Решение задачи №698:
[ 698.1 a) 5 + a2 = (a + l)(a + 6) => 5 + a2 = a2 + 6a + + a + 6 => 7a = -1 => a =
б) 2x ¦ (a - 8) = (a + l)(2a - 3) => 2a2 - 16a = 2a2 -
- 3a + 2a - 3 =Ф 15a = 3 => a = 0,2;
в) (3a — 2)(a + 4) — 3 - (a + 5)(a — 1) = 0 => 3a2 + 12a —
— 2a — 8 — За2 + 3a - 15a + 15 - 0 => 1-Oa - 12a = 8 -
- 15 => -2a = -7 =>• a = 3,5;
r) a2 + a • (6 — 2a) •= (a - 1)(2 - a) - 2 =>¦ a2 + 6a —
— 2a2 = 2a — a2 — 2 + a — 2 => 6a — 2a — a — —4 =>• =$¦ 3a = -4 => a = — 1
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