Вправи: 518 (1-4)

518. Розв’яжіть рівняння:

1) (х + 2)² – 36 = 0;

(х + 2 + 6)(х + 2 – 6) = 0;

х + 8 = 0;

х = –8;

х – 4 = 0;

х = 4.

2) (2х – 1)² – 4 = 0;

(2х – 1 + 2)(2х – 1 – 2) = 0;

2х + 1 = 0;

2х = –1;

х = –0,5;

2х – 3 = 0;

2х = 3;

х = 1,5.

3) х² – (6 + х)² = 9х;

(х + 6 + х)(х – 6 – х) – 9х = 0;

–6(2х + 6) – 9х = 0;

–12х – 9х – 36 = 0;

–21х = 36;

х = –157.

4) 25х² – (7 – 5х)² = 14х;

(5х + 7 – 5х)(5х – 7 + 5х) – 14х = 0;

7(10х – 7) – 14х = 0;

70х – 49 – 14х = 0;

56х = 49;

х = 4956.

5) (4 + 3х)² – (6х – 2)² = 0;

(4 + 3х + 6х – 2)(4 + 3х – 6х + 2) = 0;

(2 + 9х)(6 – 3х) = 0;

2 + 9х = 0;

9х = –2;

х = –29;

6 – 3х = 0;

3х = 6;

х = 2

6) (5х + 1)² – (4х + 5)² = 0.

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

(9х + 6)(х – 4) = 0;

9х + 6 = 0;

9х = –6;

х = –23;

х – 4 = 0;

х = 4.