Question

Rozwiąż równanie i przykłady są w załączniku

Answer 1

g)

x-2/ x-4  + x-3/ x – 4  = 2x -  5          x ≠ 4

(x-2 + x – 3) / x-4 = 2x – 5

(2x – 5)/x-4 = 2x – 5

(2x-5)(x-4) = 2x – 5    

2x² - 8x – 5x + 20 – 2x + 5 = 0

2x² -15x + 25 = 0

∆ = b² - 4ac

∆ = (-15)² - 4 * 2 * 25 = 225 – 200 = 25

√∆ = √25 = 5

x₁ = (-b-√∆)/2a = (15 - 5)/4  = 10/4 = 5/2 = 2 ½

x₂= (-b+√∆)/2a = (15  +5)/4  = 20/4 = 5

 

h)

(x+1)(x-5) = 2*8

x² - 5x + x – 5 – 16 = 0

x² - 4x – 21 = 0

∆ = b² - 4ac

∆ = (-4)² - 4 * 1 * (-21) =  16 +  84 = 100

√∆ = √100 = 10

x₁ = (-b-√∆)/2a = (4 - 10)/2  =  - 6/2 = - 3

x₂= (-b+√∆)/2a = (4+ 10)/2 = 14/2 = 7

 

i)

(x-1)(x+1) = (x+2) (2-x)

x² - 1 = 2x - x² + 4 – 2x

x² + x² -1 -4 = 0

2x² - 5 = 0

∆ = b² - 4ac

∆ =  - 4 *2 * (-5) =  40

√∆ = √40 = √4*10 = 2√10

x₁ = -√∆/2a =  -2√10/4 = -√10/2

x₂= √∆/2a = 2√10/4 = √10/2