Rozwiąż równania: a. I2x-1I = 7 b. 2x-x^2=0 c. (5x+3)^2 = 2 d. (4x+3)^2 = 3 e. x- 3x^2 = 0

a)  I2x-1I = 7 2x-1 >= 0,  I2x-1I = 2x-1 2x-1 =7 2x = 8 x = 4 ===== 2x-1 < 0,  (2x-1) =1-2x 1-2x = 7 -2x = 6 x = -3 ====== x = 4,  v  x = -3   b) 2x-x^2 = 0 x(2-x) = 0 x = 0 ===== lub 2-x = 0 x = 2 ===== x = 0 ,  v  x = 2   c) (5x+3)^2 = 2 25x^2 +30x+9 = 2 25x^2 +30x +7 = 0 D = 900 -(4*25*7) = 900- 700 = 200 VD =10V2 x1 =(-30 -10V2)/50 =(-3-V2)/5 x2 =(-30+10V2)/50 =(-3+V2)/5   x =(-3V2)/5,   v   x =(-3+V2)/5   d) (4x+3)^2 =3 16x^2 +24x+9 =3 16x^2 +24x+6 = 0 I:2 8x^2 +12x+3 = 0 D =144 -(4*8*3) =144-96 = 48 VD = 4V3 x1 =(-12-4V3)/16 =(-3-V3)/4 x2 =(-12+4V3)/16 =(-3+V3)/4   x =(-3-V3)/4,   v   x =(-3+V3)/4   e) x-3x^2 = 0 x(1-3x) = 0 x = 0 ===== lub 1-3x = 0 3x =1 x = 1/3 ======= x = 0,  v  x =1/3