Sh. Ismailov, A. Qo’chqorov, B. Abdurahmoi

ab ac c b ac abd

abc, bcd, —, —, —, —, abcd,

’ c ’ d ’ ad’ cd’ bd’ c

ifodalar qanday ishoralarga ega bo’ladi ?

21. 
    Agar
    

1. 
   a va b bir xil ishorali sonlar;
   
2. 
   a va b turli ishorali sonlar ekanligi ma’lum bo’lsa,
   

_a

ab ko’paytma va — kasr qanday ishoralarga ega bo’ladi ? b

21. 
    Agar
    

a) ab > 0; b) — > 0; s) ab < 0 ; d) — < 0; e) a b > 0 bb

_a

f) a b < 0; g) — < 0 ekanligi ma’lum bo’lsa, a va b sonlarning ishorasini _b2

toping.

21. 
    a > 2 ekanligi ma’lum bo’lsa, ifodaning ishorasi qanaqa ?
    

a — 2

a
a -1
) 3a - 6; b) 10 - 5a; s) 2a - 2; d) (a - 2)(1 - a); e)

f) (a - 3)²( a -1); g) _; h) .

2. 
   a (5+ a)
   

21. 
    a < 3 ekanligi ma’lum bo’lsa, ifodaning ishorasi qanday bo’ladi ?
    
22. 
    
    

a _ 4

1. 
   2a _ 6; b) 12 _ 4a; s) 2a _ 8; d) (a _ 5)(a _ 3); e)
   

3. 
   _ a
   

f) ^(a _^{1) (a} _ ²⁾; g⁾ ; ^h)

3. 
   _ a (a _ 2)(3 _ a)
   

21. 
    Agar a) a < 1; b) a > 4; s) 1 < a < 4; d)a > 5 ekanligi ma’lum bo’lsa (a _ 1)( a _ 4) ifoda qaysi ishoraga ega bo’ladi ?
    
22. 
    Agar a > 1 va b > 1 bo’lsa, u holda ab +1 > a + b ekanligini isbotlang.
    
23. 
    Agar a > b va b < 2 bo’lsa, u holda b(a + 2) > b² + 2a ekanligini
    

isbotlang.

21. 
    Agar a > b > 1 bo’lsa, u holda a²b + b² + a > ab² + a² + b ekanligini
    

isbotlang.

21. 
    Agar a < b < 2 bo’lsa, u holda a²b + 2b² + 4a < ab² + 2a² + 4b ekanligini
    

isbotlang.

21. 
    Agar 1 < a < b < 2 bo’lsa, u holda a²b _ ab² _ a² _ ab + 2b² + 2a _ 2b > 0
    

ekanligini isbotlang.

21. 
    Agar a > b > c bo’lsa, u holda a²(b _ c) + b²(c _ a) _ c² (a _ b) > 0 ekanligini
    

isbotlang.

_x³

21. 
    sinx > x (x > 0) tengsizlikni isbotlang.
    

6

21. 
    Sonlarni taqqoslang.
    

4. 
   ln2004 ln2005
   

1. 
   ) va
   

ln2005 ln2006

2. 
   cos(sin2006) va sin(cos2006)
   

21. 
    x > 0 uchun 1 + 2lnx < x² tengsizlik o’rinli bo’lishini isbotlang.
    

x₁, x₂,...,x_n musbat sonlar bo’lsin.
x₁ +... + x

1 n_

n

, а ф 0 a = 0

^f(a)

4^x1 •... •

x

funtsiyaning monoton o’suvchi bo’lishini isbotlang. Bundan tashqari f funktsiya qat’iy o’suvchi bo’ladi, faqat va faqat shu holdaki, qachonki x_] sonlarning hammasi o’zaro teng bo’lmasa.

3>/3

57.sinasin ^sin^<

8

tengsizlikni isbotlang, bu yerda а, в va у biror

uchburchakning ichki burchaklari.

58. a₁, a₂,...,a_n lar a_k e (0:12) (k = 1,.,n) va a₁ + a₂ + ... + a_n = 1 xossalarga eg

a
1

1

> (n² - 1)ⁿ ekanligini isbotlang.

1

1

V ^a1 У

V ^a2 У

v ^an У

a² + b² b² + c² a² + c² a³ b³ c³

< — + — + —

bo’lgan sonlar bo’lsin 59. Ixtiyoriy a, b, c musbat sonlar uchun

a + b + c <

2