Odpowiedź:
a) [tex]100 x^2 - 81 = 0[/tex]
(10 x)² - 9² = 0
(10 x - 9)*(10 x + 9) = 0
10 x - 9 = 0 lub 10 x + 9 = 0
10 x = 9 lub 10 x = - 9 / : 10
x = 0,9 lub x = - 0,9
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b) [tex]\frac{1}{4} x^{2} - \frac{1}{9} = 0[/tex]
( 0,5 x)² - [tex]( \frac{1}{3} )[/tex]² = 0
( 0,5 x - [tex]\frac{1}{3}[/tex] )*( 0,5 x + [tex]\frac{1}{3} ) = 0[/tex]
0,5 x = [tex]\frac{1}{3}[/tex] lub 0,5 x = - [tex]\frac{1}{3}[/tex] / * 2
x = [tex]\frac{2}{3}[/tex] lub x = - [tex]\frac{2}{3}[/tex]
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c) x² + 10 x + 25 = 0
( x + 5)² = 0
x + 5 = 0
x = - 5
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d) x² + 64 = 16 x
x²- 16 x + 64 = 0
( x - 8 )² = 0
x - 8 = 0
x = 8
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e) 24 x - x² = 144
x² - 24 x + 144 = 0
( x - 12)² = 0
x - 12 = 0
x = 12
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f ) 1 + 9 x² + 6 x = 0
( 1 + 3 x )² = 0
1 + 3 x = 0
3 x = - 1 / : 3
x = - [tex]\frac{1}{3}[/tex]
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g ) x² = (1 - x)*( 1 + x )
x² = 1² - x²
2 x² = 1 / : 2
x² = [tex]\frac{1}{2}[/tex]
x = - [tex]\frac{1}{\sqrt{2} }[/tex] lub x = [tex]\frac{1}{\sqrt{2} }[/tex]
x = - [tex]\frac{\sqrt{2} }{2}[/tex] lub x =[tex]\frac{\sqrt{2} }{2}[/tex]
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h) 0,5 x*( 6 - x) = 2 + x / * 2
x*( 6 - x) = 4 + 2 x
6 x - x² = 4 - 2 x
x² - 8 x + 4 = 0
Δ = ( -8)² - 4*1*4 = 64 - 16 = 48 = 16*3
√Δ = 4√3
x = [tex]\frac{8 - 4\sqrt{3} }{2*1} = 4 - 2\sqrt{3}[/tex] lub x = 4 + 2[tex]\sqrt{3}[/tex]
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i ) ( x - 3)*(x - 2) = 7 x - 30
x² -2 x - 3 x + 6 = 7 x - 30
x² - 12 x + 36 = 0
( x - 6)² = 0
x - 6 = 0
x = 6
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Szczegółowe wyjaśnienie:
