РЕШЕНИЯ ЗАДАНИЯ ДЛЯ ВЫПУСКНОГО ЭКЗАМЕНА ПО АЛГЕБРЕ И НАЧАЛАМ АНАЛИЗА 11-класс 5-задание

5-nji iş. Çep tarap
1.Aňlatmany ýönekeýleşdiriň:
a43-8a13 ba23+23ab+4b23:1-23ba.a13(a- 8b)(a13)2+2a13b13+(2b13)2·a13a13-(2b13) = a23(a- 8b)a- 8b=a13=3 a2 ;
Jogaby: 3 a2 ;
2.Deňlemäni çözüň:
3x-193-x=0; 3x-132x-6=0; x - 2x-6 =0;
x = 2x-6; x= 4;
Jogaby: x=4;
3.Goşa deňsizligi çözüň:
0<2+2-4x3<4; -2< 2-4x3 < 2; -6 < 2-4x< 6;
-8 < 4x < 4; -4< 4x < 8; - 1 < x < 2; x€(-1; 2); Jogaby: x€(-1; 2);

4. Kwadrat görnüşli karton listinden ini 3sm bolan zolagy kesip aýyrdylar. Listiň galan gönüburçly böleginiň meýdany 70 sm2 deň. Listiň ilkibaşdaky ölçeglerini tapyň.
Kwadrat görnüşli karton listiň ilkibaşdaky ölçegi x sm bolsun. Onda,
x(x-3) = 70; x2-3x-70=0; (x-10)(x+7)=0; x1=10, x2=-7;
x2 < 0; => x=x1=10; x=10;
Jogaby: 10sm x10sm;
5. Toždestwony subut ediň:
2 sin π4+αsinπ4-α=cos 2α.Subudy:
2 sin π4+αsinπ4-α=2·13[cos π4+α-π4+α-cos π4+α+π4-α]=
= cos 2α - cos π2 = cos 2α; Subut edildi.
6. fx=37+3x funksiýa üçin grafigi M (3; 8) nokatdan geçýän asyl funksiýany tapyň.
F(x)=fxdx=f3dx7+3x=27+3x +C; F(3)=8 => F(3)=2 16 +C=8+C=8;
C=0; F(x)=27+3x; Jogaby: F(x)=27+3x;
7. y = x 2 parabolada (3; 0) koordinataly nokada iň golaý ýerleşen nokady tapyň.
. y = x 2 ; A(x,y); B(3,0); minAB üçin A(x,y) nokady tapmaly;
S=AB=(3-x)2+y2 = 9-6x+x2+x4; S(x)= x4+x2-6x+9 ;
x€(0,3); Sˊ(x)= 2x3-x+3x4+x2-6x+9; Sˊ(x)=0; 2x3-x+3 \0;
2(x-1)( x2+x+32)=0; x=1; y= 1; min[0;3]Sx=S1= 5 ;
max[0;3]Sx=S0=3;Jogaby: (1; 1) nokat.
5-nji iş. Sag tarap
1.Aňlatmany ýönekeýleşdiriň:
3m2-2m13n13+43n23m4+83m∙n∙1+2n13m13. m132-m13(2n13)+2n132m13(m+8n) · m13+2n13m13 = m+8nm23(m+8n) = 1m23 = 13m2 ;
Jogaby: 13m2 2. Deňlemäni çözüň:
4x-0,5x-3=0; 22x-23-x=0; 2x = 3-x ; x=1;
Jogaby: x=1;
3.Goşa deňsizligi çözüň:
-3<1-3x4-3<0; 0<1-3x4<3; 0<1-3x<12; - 1<-3x<11;
-11<3x<1; - 113 < x < 1 3 ; x€(- 113; 1 3 );Jogaby: x€(- 113; 1 3 );4. Uzynlygy 120 sm bolan gönüburçluk görnüşindäki tagta böleginden tarapy gönüburçlugyň inine geň bolan kwadraty kesip aýyrdylar. Tagtanyň galan gönüburçly böleginiň meýdany 2000 sm2 deň boldy. Kwadratyň tarapyny tapyň.
Kwadratyň taraplary x sm. x(120-x) = 2000; x2-120x+2000=0;
(x-100)(x-20)=0; x1= 100; x2= 20;
Jogaby: 100 sm ýa-da 20 sm.
5. Toždestwony subut ediň:
2 cos π4+αcos π4-α=cos 2α.Subudy:
2 cos π4+αcos π4-α= 2 · 12 · [cos π4+α+π4-α +
+cos π4+α-π4+α] = cosπ2 + cos2⍶ = cos2⍶; Subut edildi.
6. fx= 43-2x 2 funksiýa üçin grafigi M -12; 116 nokatdan geçýän asyl funksiýany tapyň.
F(x)=fxdx = 4dx3-2x 2= 23-2x + C; F(-12)= - 116 ; =>
F(- 12 )= 23+1+C=12+C= 116; C= - 716; F(x)= 23-2x - 716 ;
Jogaby: F(x)= 23-2x - 716 ;
7. y=x egri çyzygyň üstünde (3; 6) koordinataly nokada iň golaý ýerleşen nokady tapyň.
y=x; A(3; 6); B(x,y); minAB üçin B(x,y) nokady tapmaly:
L =AB=(x-3)2 + (y-3)2 =(x2 -6x+ 9+x-12x+36=
= x2 -5x-12x+45 ;
Lˊ(x )= 2x-5-6x2x2 -5x-12x+45 ; Lˊ(x )= 0; 2x-5-6x =0;
x=4; y = x = 4 = 2; B(4; 2);
Jogaby: B(4; 2);