5. Rozwiąż równanie.
a) 100x2-1=0
b) 81x2-9=0
c) 7x2-21x=0
d) 5x2+8=8-x
e) 6x2+x-1=0
f) 12x2-11x+2=0
pomorze ktoś mam na jutro
a) 100x2-1=0
b) 81x2-9=0
c) 7x2-21x=0
d) 5x2+8=8-x
e) 6x2+x-1=0
f) 12x2-11x+2=0
pomorze ktoś mam na jutro
Odpowiedź:
a) 100 x² - 1 = 0
100 x² = 1 / :100
x² = [tex]\frac{1}{100}[/tex]
x = - [tex]\frac{1}{10}[/tex] lub x = [tex]\frac{1}{10}[/tex]
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b ) 81 x² - 9 = 0
( 9 x - 3)*(9 x + 3 ) = 0
9 x = 3 lub 9 x = - 3 / : 9
x = [tex]\frac{1}{3}[/tex] lub x = - [tex]\frac{1}{3}[/tex]
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c ) 7 x² -21 x = 0
7 x*(x - 3) = 0
x = 0 lub x - 3 = 0
x = 0 lub x = 3
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d ) 5 x² + 8 = 8 - x
5 x² + x = 0
x*( 5 x + 1) = 0
x = 0 lub 5 x + 1 = 0
x = 0 lub x = - [tex]\frac{1}{5}[/tex]
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e ) 6 x² + x - 1 = 0
Δ = 1² - 4*6*( - 1) = 1 + 24 = 25 √Δ = 5
x = [tex]\frac{- 1 - 5}{2*6} = - 0,5[/tex] lub x = [tex]\frac{-1 + 5}{2*6} = \frac{4}{12} = \frac{1}{3}[/tex]
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f ) 12 x² - 11 x + 2 = 0
Δ = ( - 11 )² - 4*12*2 = 121 - 96 = 25 √Δ = 5
x = [tex]\frac{11- 5}{2*12} = \frac{6}{24} = \frac{1}{4}[/tex] lub x = [tex]\frac{11 + 5}{24} = \frac{16}{24} = \frac{2}{3}[/tex]
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