Olimpiada VII tur yechimlari (7-sinf)

1.Yechish:

X⁸+x+1=(x⁸+x⁷+x⁶)-(x⁷+x⁶+x⁵)+(x⁵+x⁴+x³)-(x⁴+x³+x²)+(x²+x+1)= x⁶(x²+x+1)-

-x⁵(x²+x+1)+x³(x²+x+1)-x²(x²+x+1)+ (x²+x+1)=(x⁶-x⁵+x³-x²+1) (x²+x+1).

2. Yechish:

<RLS=80%<PLR  ,  <PLR= x deylik , u holda <RLS= 0,8x bo’ladi.Tenglama tuzamiz: x+0,8x= 180;   1,8x= 180;  x= 180:1,8= 100;   180-100= 80;

Javob: 100⁰; 80⁰.

3. Yechish:

= 2⁴= 16  ⇒ 22²> ;

2²²= 2⁴ ⋅2¹⁸= 16⋅ 2¹⁸ > ;

2²²= 2⁹ ⋅2¹³= 512⋅ 2¹³>22², chunki 22² =484.   Javob: 2²²> 22²> .

4. Javob: 45 va 90.
5. Yechish:(a²-9)x=7a²-20a-3;        (a-3)(a+3)x= (7a+1)(a-3). Bundan:

Javob:  a=3 da , x∈ R; a= -3 da , ildizi yo’q;  a  ±≠3 da  .

6. Yechish:

y= ax+5;   M(-3;2)     M ning koordinatalarini tenglikka qo’yamiz, unda

a (-3)+5=2;   a=1;       J: a= 1.

7.Yechish:

 belgilash kiritamiz , u holda    Bu yerdan a= 0,25;   b= 0,05 topilganlarni o’rniga qo’yilsa,   x=6; y= 2 chiqadi.            Javob: x=6; y=2.

8.Yechish:

(x+3)(y-2)=0;   Tenglamaning ildizlari x=-3 va y=2 . Grafik x=-3 oy o’qiga parallel va ox o’qida  x=-3dan o’tadigan to’g’ri chiziq. y= 2 to’g’ri chiziq esa, oy da y=2 dan o’tuvchi ox o’qiga paralleldir.

9.Yechish:

  ; 9x= 896-7x;  16x=896;  x= 56;  128-56=72;   J: 56; 72.

10. Yechish: