Question

Prosze o rozwiązanie tych zadań

Answer 1

Odpowiedź:

zad 1

a)

2x² - x⁴ + 3x⁴ - 7 - 2x⁴ - 5x³ = - 5x³ + 2x² - 7 =

= - 5 * (- 2)³ + 2 * (- 2)² - 7 = - 5 * (- 8) + 2 * 4 - 7 = - 40 + 8 - 7 = - 39

b)

1/2x⁵ + x⁴ - 1/3x⁵ + 2x - x⁴ - 1/6x⁵ + 3 =

= 3/6x⁵ - 2/6x⁵ + 2x - 1/6x⁵ + 3 = 2x + 3 = 2 * (- 2) + 3 = - 4 + 3 = - 1

zad 2

x = - 1/2 oraz x = 1/4

dla x = - 1/2

a)

4x² - 8x = 4 * (- 1/2)² - 8 * (- 1/2) = 4 * 1/4 + 4 = 1 + 4 = 5

b)

- 8x³ + 2x = - 8 * (- 1/2)³ + 2 * (- 1/2) = - 8 * (- 1/8) - 1 = 1 - 1 = 0

c)

16x⁴ - x² = 16 * (- 1/2)⁴ - (- 1/2)² = 16 * 1/16 - 1/4 = 1 - 1/4 = 3/4

dla x = 1/4

a)

4x² - 8x = 4 * (1/4)² - 8 * 1/4 = 4 * 1/16 - 2 = 1/4 - 2 = - 1 3/4

b)

- 8x³ + 2x = - 8 * (1/4)³ + 2 * 1/4 = 8 * 1/64 + 1/2 = 1/8 + 1/2 =

= 1/8 + 4/8 = 5/8

c)

16x⁴ - x² = 16 * (1/4)⁴ - (1/4)² = 16 * 1/256 - 1/8 = 1/16 - 1/8 =

= 1/16 - 2/16 = - 1/16

zad 3

a)

(1 + 2x)(1 - 2x) = 1 - 4x²

b)

(3x - 7)(7 + 3x) = (3x - 7)(3x + 7) = 9x² - 48

c)

(4x +3)(3 - 4x) = (3 + 4x)(3 - 4x) = 9 - 16x²

d)

(x + 6)² = x² + 12x + 36

e)

(2x - 1)² = 4x² - 4x + 1

f)

(x² + 2)² = x⁴ + 4x² + 4

g)

(x -2x²)² = x² - 4x³ + 4x⁴