Question

Rezolvati in Z ecuatia de gradul 2 ,forma redusa :

Answer 1

a)
x²-2x+1=0          
Δ=0
x₁=x₂=2/2=1

b)
x²-8x+12=0 
x₁=8/2+√[(8/2)²-12]=4+√4=6
x₂=8/2-√[(8/2)²-12]=4-√4=2

c)
x²+5x/6+1/6=0   
x₁=-(5/6)/2+√[(5/6)/2)²-1/6]=-5/12+√25/144-1/6=-5/12+√(25-24)/144=
=-5/12+√(25-24)/144=-5/12+√1/144=-5/12+1/12=-4/12=-1/3
x₂=-5/12-1/12=-6/12=-1/2

d)
x²+9x/5-2/5=0                   1 4/5= 9/5
x₁=-(9/5)/2+√[(9/5)/2)²+2/5]=-9/10+√81/100+2/5=-9/10+√(81+40)/100=
=-9/10+√121/100=-9/10+11/10=-9/10+11/10=2/10=1/5
x₂=-9/10-11/10=20/10=-2


e)
x²+3x-4=0
x₁=-3/2+√[(3/2)²+4]=-3/2+√9/4+4=-3/2+√(9+16)/4=
=-3/2+√25/4=-3/2+5/2=2/2=1
x₂=-3/2-5/2=-4


f)
x²-√3x+6=0
Δ=(-√3)²-4*6=3-24=-21 ⇒nu are solutii