1 Rozwiąż równanie. a) 9 - x2 = 0 b) 5x2 = 125 - e) x2 – 7x+6= 0 f) x - 2x2 = x?- 4 c) x2 – 5x = 0 d) 4x - 3x2 = 0​



Odpowiedź :

a)

[tex]9-x^{2} = 0\\\\(3+x)(3-x) = 0\\\\3+x = 0 \ \vee \ 3-x = 0\\\\x = -3 \ \vee x = 3[/tex]

b)

[tex]5x^{2}=125 \ \ /:5\\\\x^{2} = 25\\\\x^{2}-25 = 0\\\\(x+5)(x-5) = 0\\\\x+5 = 0 \ \vee \ x - 5 = 0\\\\x = -5 \ \vee \ x = 5[/tex]

c)

[tex]x^{2}-5x = 0\\\\x(x-5) = 0\\\\x = 0 \ \vee \ x - 5 = 0\\\\x = 0 \ \vee \ x = 5[/tex]

d)

[tex]4x - 3x^{2} = 0\\\\x(4-3x) = 0\\\\x = 0 \ \vee \ 4-3x = 0\\\\x = 0 \ \vee \ -3x = -4\\\\x = 0 \ \vee \ x = \frac{4}{3}[/tex]

e)

[tex]x^{2}-7x = 0\\\\x(x-7) = 0\\\\x = 0 \ \vee \ x-7 = 0\\\\x = 0 \ \vee \ x = 7[/tex]