Parametriani Machvenebliani Gantoleba
y ≡ nx n > 0 ⇐⇒ y > 0
ay 2 + by + c = 0
T u Gantolebas Aqvs 2 Amonaxsni :






 








 
D > 0 =⇒ b2 − 4ac > 0 =⇒ b2 > 4ac


 −b > 0
 y1 + y2 > 0
y1 > 0
a
=⇒
=⇒ 
c


 y y > 0
y2 > 0
1 2
a >0
Sabolood M iviget







b2 > 4ac
− ab > 0





 c > 0
a
1
T u Gantolebas Aqvs 1 Amonaxsni :



D>

 
 y
1



  y
2
P irveli Shemtxveva :
0 =⇒ b2 > 4ac
<0
=⇒ y1 y2 < 0 =⇒
>0
c
a
<0
M eore Shemtxveva :
D = 0 =⇒ b2 = 4ac
 y > 0 =⇒ − b > 0
2a


M esame Shemtxveva :

 a = 0
 y > 0 =⇒ − c > 0
b
P asuxi Iqneba Samive Shemtxveva
Anu Sabolood P asuxi Gamodis :
I − b2 > 4ac
II − b2 = 4ac
III − a = 0
c
<0
a
b
>0
2a
c
− >0
b
−
Am Ori P asuxis Gaertianeba
Am Ori P asuxis Gaertianeba
Am Ori P asuxis Gaertianeba
2
T u Gantolebas Ar Aq Amonaxsni
P irveliShemtxveva :
D < 0 =⇒ b2 < 4ac
M eoreShemtxveva :
D = 0 =⇒ b2 = 4ac
 y < 0 =⇒ − b < 0
2c





D>

 
 y
1



  y
2
M esameShemtxveva :
0 =⇒ b2 > 4ac

 y +y <0
 −b < 0
<0
1
2
=⇒ 
=⇒  c a
<0
y 1 y2 > 0
a <0
P asuxi Iqneba Samive Shemtxveva
Anu Sabolood P asuxi Gamodis :
I − b2 < 4ac
b
<0
Am Ori P asuxis Gaertianeba
2a
b
c
III − b2 > 4ac − < 0
<0
Am Sami P asuxis Gaertianeba
a
a
II − b2 = 4ac
−
3
Machvenebliani Utoloba



ax > b
0 < a < 1 =⇒ x < loga b
a > 1 =⇒ x > loga b
Logaritmebi
logc ab = logc a + logc b
a
logc = logc a − logc b
b
logc an = n logc a
√
1
logc n a = logc a
n
1
logcn a = logc a
n
√
log n c a = n logc a
loga b =
1
logc b
=
logb a logc a
c
loga (ab + c) = 1 + loga (b + )
a
Logaritmuli utolobebi
loga b =⇒ a > 0 a ̸= 1 b > 0


loga x > b =⇒ 
0 < a < 1 =⇒ x < ab
a > 1 =⇒ x > ab
4