Вправи: 401

401. Розв’яжіть рівняння:

1) х² + (2 – х)(х + 1) = 0;

х² + 2х + 2 – х² – х = 0;

х = 2.

2) х² + (4 – х)(х – 1) = 0;

х² + 4х – 4 – х² + х = 0;

5х = 4;

х = 0,8.

3) (5 – х)(х + 6) + х(х – 8) = 0;

5х + 30 – х² – 6х + х² – 8х = 0;

9х = 30;

х = 313.

4) (х + 1)(x – 1) + (9 – х)(х – 2) = 0;

х² – х + х – 1 + 9х – 18 – х² + 2х = 0;

11х = 19;

х = 1811.

5) (4 – х)(4х – 3) + (1 + 2х)(2х – 1) = 0;

16х – 12 – 4х² + 3х + 2х – 1 + 4х² – 2х = 0;

19х = 13;

х = 1319.

6) (х – 5)(х – 2) – (х + 1)(х + 8) = 0;

х² – 2х – 5х + 10 – х² – 8х – х + 8 = 0;

16х = 18;

х = 118.

7) (х – 1)(х + 1) – (х – 3)(х – 2) = 0;

х² + х – х – 1 – х² + 2х + 3х – 6 = 0;

5х = 7;

х = 125.

8) (х – 3)(х – 4) = (х – 8)(х – 1);

х² – 4х – 3х + 12 = х² – х – 8х + 8;

х² – 4х – 3х – х² + х + 8х = 8 – 12;

2х = –4;

х = –2.