Question

Rozwiąż równanie.
a)x²-2x=0
b)3x²+8x=0
c)4x²-x/2=0
d)x²=-7x
e)-5x-4x²=0
f)1/3x²=5x
g)-2/7x²+2x=0
h)x²+2/2=4x+1

Answer 1

A)x²-2x=0
x(x-2)=0
x=0
lub x=2

b)3x²+8x=0
x(3x+8)=0
3x+8=0 lub x=0
3x=-8
x=-2⅔

c)4x²-x/2=0
x(4x-½)=0
4x-½=0
lub x=0
4x=½
x=¹/₈

d)x²=-7x
x²+7x=0
x(x+7)=0
x=0 lub x=-7

e)-5x-4x²=0
x(-5-4x)=0
-4x=5
lub x=0
x=-⁵/₄=-1¼

f)1/3x²=5x
⅓x²-5x=0
x(⅓x-5)=0
⅓x=5 lub x=0
x=15

g)-2/7x²+2x=0
x(-²/₇x+2)=0
-²/₇x=-2 lub x=0
x=7

h)x²+2/2 =4x+1
h)x²+2/2-4x-1=0
x²-4x=0
x(x-4)=0
x=4
lub x=0

Answer 2

A)
x²-2x = 0
x(x - 2) = 0
x = 0 v x - 2 = 0
x = 0 v x = 2
x₁ = 0 i x₂ = 2

b)
3x²+8x = 0
x(3x + 8) = 0
x = 0 v 3x + 8 = 0
x = 0 v 3x = - 8 /:3
x = 0 v x = -⁸/₃ = -2⅔
x₁ = 0 i x₂ = -2⅔

c)
4x²-x/2 = 0 /*2
8x² - x = 0
x(8x - 1) = 0
x = 0 v 8x - 1 = 0
x = 0 v 8x = 1 /:8
x = 0 v x = ⅛
x₁ = 0 i x₂ = ⅛

d)
x² = -7x
x² + 7x = 0
x(x + 7) = 0
x = 0 v x + 7 = 0
x = 0 v x = -7
x₁ = 0 i x₂ = -7

e)
-5x-4x² = 0
x(-5 - 4x) = 0
x = 0 v -5 - 4x = 0
x = 0 v -4x = 5 /:(-4)
x = 0 v x = - ⁵/₄ = - 1¼
x₁ = 0 i x₂ = - 1¼
f)
⅓x² = 5x /*3
x² = 15x
x² - 15x = 0
x(x - 15) = 0
x = 0 v x - 15 = 0
x = 0 v x = 15
x₁ = 0 i x₂ = 15

g)
-²/₇x² + 2x = 0 /*(-⁷/₂)
x² - 7x = 0
x(x - 7) = 0
x = 0 v x - 7 = 0
x = 0 v x = 7
x₁ = 0 i x₂ = 7

h)
x²+2/2 = 4x + 1 / *2
x² + 2 = 8x + 2
x² + 2 - 8x - 2 = 0
x² - 8x = 0
x(x - 8) = 0
x = 0 v x - 8 = 0
x = 0 v x = 8
x₁ = 0 i x₂ = 8