Question

Zadanie Domowe
1. Rozwiąż równania
a) x^{2} -25=O
b) 6 x^{2} -7 x^{2} =5
c)6 x^{2} =x+1
d) 13-2 x=- x^{2}
e) -9 x^{2} +2x-=0
f) x^{2} -5x=0

Answer 1

A)
x^2 - 25 = 0
(x + 5)(x - 5) = 0
x + 5 = 0
x = - 5
lub
x - 5 = 0
x = 5
x = -5  v  x = 5

b)
6x^2 - 7x^2 = 5
-x^2 = 5    I*(-1)
x^2 = -5, sprzeczność, brak rozwiazań

c)
6x^2 = x + 1
6x^2 - x - 1 = 0
D = b^2 - 4ac = 1 + 24 = 25
VD = 5
x1 = (-b - VD)/2a = (1 - 5)/12 = - 4/12 = -1/3
x2 = (-b + VD)/2a = (1 + 5)/12 = 6/12 = 1/2
x = -1/3  v  x = 1/2

d)
13 - 2x = - x^2
x^2 - 2x + 13 = 0
D = 4 - 52 = -48
D < 0, brak rozwiązań

e)
-9x^2 + 2x - 1/9 = 0    I*(-9)
81x^2 - 18x + 1 = 0
D = 324 - 324 = 0
xo = -b/2a = -(-18)/162 = 18/162 = 1/9
xo = 1/9

f)
x^2 - 5x = 0
x(x - 5) = 0
x = 0
lub
x - 5 = 0
x = 5
x = 0  v  x = 5