Вправи: 595

595. Розв’яжи рівняння.

а) (x³ + 3)(х⁶ – 3x³ + 9) – 26 = 0;

(x³)³ + 3³ = 26;

x⁹ + 27 = 26;

x⁹ = 26 – 27;

x⁹ = –1;

x = –1.

б) (x – 2)(x² + 2x + 4) – (x + 4)(x² – 4x + 16) = 6(2x – 9);

x³ – 2³ – (x³ + 4³) = 12x – 54;

x³ – 8 – x³ – 64 = 12x – 54;

12x – 54 = –72;

12x = –18| : 12;

x = –1,5.

в) (x + 5)(x² – 5x + 25) – x(х – 4)(x + 4) = –3;

x³ + 5³ – x(x² – 16) = –3;

x³ + 125 – x³ + 16x = –3;

16х = –3 – 125;

16х = –128| : 16;

x = –8.

г) (x² – 4)(x² – 2x + 4) = x³(x – 2);

(x – 2)(x + 2)(x² – 2x + 4) = x³(x – 2);

(x – 2)(x³ + 2³) = x³(x – 2);

(x – 2)(x³ + 8) – x³(x – 2) = 0;

(x – 2)(x³ + 8 – x³) = 0;

(x – 2) • 8 = 0;

8х – 16 = 0;

8х = 16 | : 8;

x = 2.