Rozwiąż równania a) 4/9x² - x + 9/16 = 0 b) x³ + 10x² + 25x = 0 c) -3x² = -12x d) 16x² - 1 = 0
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A) (2/3 x)²-2*2/3*3/4 x+(3/4)²=0 (2/3 x-3/4)²=0 2/3 x=3/4 /:2/3 x=3/4*3/2 x=9/8 b) x(x²+10x+25)=0 x=0 v (x+5)²=0 x=0 v x=-5 c) -3x²=-12x /:(-3) x²-4x=0 x(x-4)=0 x=0 v x-4=0 x=0 v x=4 d) 16x²-1=0 (4x+1)(4x-1)=0 4x+1=0 v 4x-1=0 x=-1/4 v x=1/4
(2/3 x)²-2*2/3*3/4 x+(3/4)²=0
(2/3 x-3/4)²=0
2/3 x=3/4 /:2/3
x=3/4*3/2
x=9/8
b)
x(x²+10x+25)=0
x=0 v (x+5)²=0
x=0 v x=-5
c)
-3x²=-12x /:(-3)
x²-4x=0
x(x-4)=0
x=0 v x-4=0
x=0 v x=4
d)
16x²-1=0
(4x+1)(4x-1)=0
4x+1=0 v 4x-1=0
x=-1/4 v x=1/4