Вправи: 841

841. Знайди корені рівняння.

a) 4 – (x – 3)² = 0;

22 – (x – 3)² = 0;

(2 – (x – 3))(2 + x – 3) = 0;

(2 – x + 3)(x – 1) = 0;

(5 – x)(x – 1) = 0;

5 – x = 0 або x – 1 = 0;

x = 5 x = 1.

б) (5x + 4)² = 196;

(5x + 4)² – 196 = 0;

(5x + 4)² – 14² = 0;

(5x + 4 – 14)(5x + 4 + 14) = 0;

(5x – 10)(5x + 18) = 0;

5x – 10 = 0 або 5x + 18 = 0;

5x = 10 або 5x = –18;

x = 2 або x = –3,6.

в) (3x – 2)² – (x + 6)² = 0;

(3x – 2 – (x + 6))(3x – 2 + x + 6) = 0;

(3x – 2 – x – 6)(4x + 4) = 0;

(2x – 8)(4x + 4) = 0;

2x – 8 = 0 або 4x + 4 = 0;

2x = 8 або 4x = –4;

x = 4 x = –1.

г) (2x – 1)² = (4 –5x)²;

(2x – 1)² – (4 – 5x)² = 0;

(2x – 1 – (4 – 5x))(2x – 1 + 4 – 5x) = 0;

(2x – 1 – 4 + 5x)(3 – 3x) = 0;

(7x – 5)(3 – 3x) = 0;

7x – 5 = 0 або 3 – 3x = 0;

7x = 5 або –3x – 3|: (–3);

x = 57 або х = 1.

ґ) (2x + 1)(4x² – 2x + 1) = 4x(2x² – 5);

8x³ – 4x² + 2x + 4x² – 2x + 1 = 8x³ – 20x;

20x = –1;

x = –0,05.

д) x(8x² – 5) = (4x² – 10x + 25)(2x + 5);

8x³ – 5x = 8x³ – 20x² + 50x + 20x² – 50x + 125;

–5x = 125|: (–5);

x = –25.