I Tavi

I
Tavi
32
amovxsnaT
formuliT
(3x 2 – 7x = 0) ⇔
⇔ (3x 2 – 7x + 0 = 0)
x =
7 + 7
x = 1 6
7 – 7
x = 2 6
= 7
3
= 0
sruli kvadratuli
gantolebis
amoxsnisas
sasurvelia b da
c koeficientebi
iyos mTeli
ricxvebi, xolo a _
naturaluri ricxvi.
e.i. CarCos sigane 3 sm-ia (x = –18 amocanis amonaxsenad ar gamogvadgeba,
radgan sigrZe yovelTvis arauaryofiTi ricxviT
gamoisaxeba).
magaliTi 1
ramdeni amonaxseni aqvs kvadratul gantolebas?
a) 5x2 – 7x – 1 = 0; b) 2x2 + 3x + 9 = 0.
amoxsna:
a) a = 5; b = –7; c = –1. b) a=2; b=3; c=9.
D = (–7) 2 – 4·5(–1) = 49 + 20 > 0 D = 32 – 4·2·9 = 9–72 < 0
gantolebas aqvs ori gansxvavebuli gantolebas amonaxseni
amonaxseni; ara aqvs.
magaliTi 2
amoxseniT gantoleba:
a) 3x2 =7x; b) 0,7x2 - 1,3x - 2 = 0; g) 3x2 - 4x - 4 = 0.
amoxsna:
a) (3x2 = 7x) ⇔ (3x2 x = 0 x = 0
-7x=0) ⇔ (x(3x-7)=0) ⇔
3x – 7 = 0 ) ⇔
x = 7 ). x∈{0;21
3
3 }
b) (0,7x2 -1,3x - 2 = 0 |⋅10) ⇔ (7x2 - 13x - 20 = 0)
a = 7; b = -13; c = -20.
D=(–13) 2 - 4·7·(–20) = 169 + 560 = 729
x =
13 ±
14
13 + 27
x = = 1 14
20
7 ; x 13 – 27
= = –1. x∈{2 2 14
6
7 ;–1}
g) a=3; b=-4; c=-4. radgan b luwi ricxvia, amitom visargebloT (4)
formuliT:
D
4 = (– 4
2 ) 2
– 3(–4) = 4+12 = 16.
2 ±
x =
3
2 + 4
x = 1 3 = 2; x 2 – 4
= 2 3
amocana 3
= – 2 . x∈{2;– 2
3 3 }
wyalsadenis avzi ori miliT 2 sT 55 wuTSi ivseba. calke pirveli
mili mas 2 saaTiT ufro swrafad avsebs, vidre calke meore mili.
ra dro dasWirdeba TiToeul mils cal-calke avzis asavsebad?
amoxsna:
2 sT 55 wT = 255 sT = 211
60 12 sT.
vTqvaT, marto pirveli mili avzs x saaTSi avsebs, maSin marto
meore mili avzs (x+2) saaTSi aavsebs. 1 saaTSi pirveli mili aavsebs
avzis 1
x
nawils, xolo meore mili – 1
x+2
nawils. orive mili 211
12