Irratsional tenglama va tengsizliklarni yechish. Reja

2. Irratsional tengsizlik va ularni yechish.

1-misol: 2(x-1)< tengsizlikni yeching.

Yechish:

Chet ildiz hosil bo’lmasligi uchun bunday mulohaza yuritamiz:

a) x<1 da chap tomon manfiy; o’ng tomon manfiy emas. Demak,

b) x1 da chap va o’ng tomonlar musbat. 4x²-8x+4<4x²+23x+15; . Bu holda yechim yo’q.

Javob:
2-misol: x³+x²+2>4 tengsizlikni yeching.

Yechish: f(x)= x³+x²+2-4 funksiya [0;) oraliqda o’suvchi va aniqlangan bo’lib, f(1)=0 bo’lganidan x>1 bo’ladi. Demak, yechim (1; ) oraliqdan iborat.

3-misol. (x-4) tengsizlikni yeching.

Yechish: Bu tengsizlikni yechish unga teng kuchli bo’lgan

sistemani yechish bilan bog’liq.

Demak, yechim {(-;4](- ;-2][1; )}=(-;-2] [1;4]

Yuqoridagilardan ba’zan irratsional tengsizliklarni yechish tengsizliklar sistemasini yechish bilan ekvivalent bo’lishi mumkinligi ko’rinadi.

Mustaqil yechish uchun misollar:

1. 
   5+>7;
   
2. 
   x+<8;
   
3. 
   >3;
   
4. 
   <4;
   
5. 
   >1.
   

Tayanch iboralar:

irratsional, tenglama, tengsizlik, musbat, manfiy, chet ildiz

Nazorat savollari:
Tenglamalarni yeching:

1.

2.

3.

4.

Tengsizlikni yeching

1.

2.

3.

Test savollari
1. tenglamani yeching.
A) 6

B) 5

C) -9
2. tenglamani yeching.

1. 
   -2;5
   
2. 
   2;5
   
3. 
   -5;2
   

3. tengsizlikni yaching
A)

B)

C)

4. tenglamani yeching.

A) – 1 B) – 2 C) 2 D) 0

E) to’g’ri javob berilmagan

5. Agar bo’lsa, х + у ni toping.