Вправи: 594

594. Розв’яжи рівняння.

а) (x² + 1)(x⁴ – x² + 1) = 1;

(x²)³ + 1³ = 1;

x⁶ + 1 = 1;

x⁶ = 1 – 1;

x⁶ = 0;

x = 0.

б) (x + 3)(x² – 3х + 9) – (x – 5)(x² + 5x + 25) = 4(20 – x);

x³ + 3³ – (x³ – 5³) = 80 – 4x;

x³ + 27 – x³ + 125 = 80 – 4x;

80 – 4x = 152;

4x = 80 – 152;

4x = –72;

x = –18.

в) (x – 2)(x² + 2x + 4) – x(х + 3)(х – 3) = 1;

x³ – 2³ – x(x² – 9) = 1;

x³ – 8 – x³ + 9x = 1;

9x = 1 + 8;

9x = 9;

x = 1.

г) (4x² – 1)(4x² – 2x + 1) = 8x³(2x – 1);

(2x – 1)(2x + 1)(4x² – 2x + 1) = 16x⁴ – 8x³;

(2x – 1)((2x)³ + 1³) = 16x⁴ – 8x³;

(2x – 1)(8x³ + 1) = 16x⁴ – 8x³;

16x⁴ + 2х – 8x³ – 1 = 16x⁴ – 8x³;

2x = 1;

x = 0,5.