Question

Rezolvati ecuațiile
a)×^2-3×+7=0
b)5×^2-9×-12=0
c)×^2-4×+4=0
d) (×-3) (×+7)=0
Ajutooorrrr..

Answer 1

a) x²-3x+7=0
x(x-3)+7= 0
x(x-3) = 0-7
x·(x-3) = -7
x= -7/(x-3)

b)5x²-9x-12=0
x(5x-9)-12= 0
x(5x-9)=0+12
x(5x-9) = 12
x = 12/(5x-9)

c)x²-4x+4=0
x( x-4)+4 = 0
x(x-4) =0-4
x(x-4) = -4
x= -4/(x-4)

d) (x-3)(x+7)=0
x²+7x-3x-21 =0
x²+4x-21=0
x(x+4)-21=0
x(x+4)=0+21
x(x+4)=21
x=21/(x+4)

Answer 2

a) x²-3x+7=0
a=1
b=-3
c=7
∆=b²-4ac=9-4·8=9-28=-19
∆<0 → ecuația nu are soluții reale

b)5x²-9x-12=0
a=5
b=-9
c=-12
∆=b²-4ac=81-4·5·(-12)=81+240= 321
x1,2=(-b±√∆)/2a=(9±√321)/2·5
x1=(9+√321)/10
x2=(9-√321)/10

c)x²-4x+4=0
a=1
b=-4
c=4
∆=b²-4ac=16-4·1·4=16-16=0
x=-b/2a=-(-4)/2=4/2=2

d) (x-3) (x+7)=0
I) x-3=0 →x=3
II) x+7=0 → x=-7