Question

Rezolvati urmatoarele ec. De gradul 2 b.d.f

Answer 1

b)
(x²-3)/2-6x=5
x²-3-12x=10
x²-12x-13=0
Δ=12²-4*(-13)=144+52=196
x₁=(12+√196)/2=(12+14)/2=13
x₁=(12-√196)/2=(12-14)/2=-2/2=-1

d)(3x²+x)/4-(2-7x)/5=(3x²+17)/10
15x²+5x-8+28x=6x²+34
9x²+33x-42=0
Δ=33²-4*(-42)*9=1089+1512=2601
x₁=(-33+√2601)/2*9=(-33+51)/18=1
x₁=(-33-√196)/2*9=(-33-51)/18=-84/18=-14/3


f)
(x+2)(x-5)/3-(11x+12)/10=2-(x-2)/3
(x²+2x-5x-10)/3-(11x+12)/10=2-(x-2)/3
(x²-3x-10)/3-(11x+12)/10=2-(x-2)/3
10x²-30x-100-33x-36=60-10x+20
10x²-63x-136=80-10x
10x²-53x-216=0
Δ=53²-4*(-216)*10=2809+8640=11449
x₁=(53+√11449)/2*10=(53+107)/20=8
x₁=(53-√11449)/2*10=(53-107)/20=-54/20=-27/10