Question

zadanie matematyka liczby rzecztwiste zadania w załączniku 6 i 7 i druga kartka

Answer 1

6. a) |x-2| = √2

x-2 = √2 ∧ x-2 = -√2

x = √2+2 ∧ x - 2 = -√2 + 2

 

b) |x+3| = 0

x + 3 = 0

x = -3

 

c) |5x - 3| = 0,4

5x - 3 = 0,4 ∧ 5x - 3 = - 0,4

5x = 3,4 ∧ 5x = 2,6

x = 0,68 ∧ x = 0,52

 

d) √[(x+3)²] = 2

|x+3| = 2

x + 3 = 2 ∧ x +3 = -2

x = -1 ∧ x = -5

 

e) √[49-14x+x²] = 1

√[(x - 7)²] = 1

|x-7| = 1

x-7 = 1 ∧ x - 7 = -1

x = 8 ∧ x = 6

 

7. a) |x+3| ≥ 5

x + 3 ≥ 5 ∧ x + 3 ≤ -5

x ≥ 2 ∧ x ≤ -8

 

b) |x-2| < 1

x - 2 < 1 ∧ x - 2 > -1

x < 3 ∧ x  > 1

 

c) √[36+12x + x²] ≤ 6

√[(x+6)²] ≤ 6

|x+6| ≤ 6

x + 6 ≤ 6 ∧ x + 6 ≥ -6

x ≤ 0 ∧ x ≥ -12

 

Kartka.

a) |x+2| = 3

x + 2 = 3 ∧ x + 2 = -3

x = 1 ∧ x = -5

 

b) |x-3| ≤ 2

x - 3≤ 2 ∧ x - 3 ≥ -2

x ≤ 5 ∧ x ≥ 1

 

c) |x+3| > 1

x + 3 > 1 ∧ x + 3 < -1

x > -2 ∧ x < -4

_____

 

a) √[x² - 3x + ⁹/₄] ≤ ¾

√[(x - ³/₂)²] ≤ ¾

|x-³/₂| ≤ ¾

x - ³/₂ ≤ ¾ ∧ x - ³/₂ ≥ -¾

x ≤ ⁹/₄ ∧ x ≥ ¾

 

b) √[9 - 6x + x²] > 2

√[(x - 3)²] > 2

|x-3| > 2

x - 3 > 2 ∧ x - 3 < -2

x > 5 ∧ x < 1