Question

Równania kwadratowe.

Rozwiąż równania.

a)3x²-4x=39

b)9x²+9x=4

c) (x+1)(2x+3)=4x²-22

d) (2x-3)²=8x

e) (1+3x)²+3x-4x²=9

f)1/9x²-1 ⅓x=-2

g)2/9x²+7/30x=1,3

h)⅓x²-4½x+15=0

i) (x+6)(x-2)=9

j)2(3x-1)+x(x+3)=8x

Answer 1

a)

3x2-4x-39=0

∆=b2-4ac

∆=(-4)2-4*3*(-39)=484

√∆=22

X1= -b-√∆/2a            lub     x2=-b+√∆

X1=4-22/2*3                       x2=4+22/2*3

X1=-3                                    x2=4 1/3

 

b)

9x2+9x-4=0

∆=9x2-4*9*(-4)=225

√∆=15

X1= -b-√∆/2a            lub     x2=-b+√∆

X1=-9-15/2*9                       x2=-9+15/2*9

X1=-1 1/3                                    x2=1/3

 

 

c)

(x+1)(2x+3)=4x2-22

2x2+3x+2x+3-4x2+22=0

-2x2+5x+25=0

∆=52-4*(-2)*25=225

√∆=15

X1= -b-√∆/2a            lub     x2=-b+√∆

X1=-5-15/2*(-2)                    x2=-5+15/2*(-2)

X1=5                                   x2=-2  1/2

 

 

d)

4x2-6x-6x+9-8x=0

4x2-20x+9=0

∆=(-20)2-4*4*9=256

√∆=16

X1= -b-√∆/2a            lub     x2=-b+√∆

X1=20-16/2*4                    x2=20+16/2*4

X1=1/2                                  x2=4  1/2

 

 

Answer 2

zalacznik