Вправи: 589 (1-3)

589. Розв’яжіть рівняння:

1) а³ – а = 0;

a(a² – 1) = 0;

a = 0;

a² – 1 = 0;

a² = 1;

a = 1; a = –1.

2) –16b⁴ + b² = 0;

b² – 16b⁴ = 0;

(b – 4b²)(b + 4b²) = 0;

b – 4b² = 0;

b(1 – 4b) = 0;

b = 0; 1 – 4b = 0;

4b = 1;

b = 0,25;

b + 4b² = 0;

b(1 + 4b) = 0;

b = 0; 1 + 4b = 0;

4b = –1;

b = –0,25.

3) 4x⁵ – 4х = 0;

4x(x⁴ – 1) = 0;

4x = 0;

x = 0;

x⁴ – 1 = 0;

x⁴ = 1;

x = –1; x = 1.

4) 5n⁶ – 6n⁵ = 0;

n⁵(5n – 6) = 0;

n⁵ = 0;

n = 0;

5n – 6 = 0;

5n = 6;

n = 1,2.

5) –t³ – 16t² – 64t = 0;

t³ + 16t² + 64t = 0;

t(t² + 16t + 64) = 0;

t(t + 8)² = 0;

t = 0;

t + 8 = 0;

t = –8.

6) (2x – 1)² – 25 = 0;

(2x – 1 – 5)(2x – 1 + 5) = 0;

(2x – 6)(2x + 4) = 0;

2x – 6 = 0;

2x = 6;

x = 3;

2x + 4 = 0;

2x = –4;

x = –2.

7) x² – (3 + х)² = 0;

(x – 3 – x)(x + 3 + x) = 0;

–3(x + 3 + x) = 0;

–3x – 9 – 3x = 0;

–6x = 9;

x = –1,5.

8) (2x – 6)² – (5х + 1)² = 0;

(2x – 6 – 5x – 1)(2x – 6 + 5x + 1) = 0;

(–3x – 7)(7x – 5) = 0;

3x + 7 = 0;

3x = –7;

x = –213;

7x – 5 = 0;

7x = 5;

x = 57.