მასწავლებლის წიგნი

MA+MB=5√2 , TviT AB monakveTis sigrZec _ AB=5√2 , amrigad M∈AB.Tu AB wrfis gantolebaa y=kx+b, maSinZ][]\2=k⋅0+b–3=–5k+b, saidanac b=2, k=1.y=x+2 wrfis abscisaTa RerZTan gadakveTis wertilia (–2;0). pasuxi: x=–2.II xerxi. aviyvanoT mocemuli gantoleba kvadratSi: √x 2 +10x+34 2 =(5√2 –√x 2 +4) 2 .gamartivebis Semdeg gantoleba CavweroT ase: √ 2(x 2 +4) =2–x,misi kvadratSi ayvaniT miviRebT: x=–2.b) mocemul tolobas SeiZleba aseTi geometriuli warmodgena davukavSiroT:I da III sakoordinato kuTxeebis biseqtrisaze (y=x wrfeze) mdebare M wertilidanA(1;6) da B(4;2) wertilebamde manZilebis jami 5-ia. vipovoT yvela aseTi wertili.Tu AB wrfis gantolebaa y=kx+b, maSinZ][]\6=k+b2=4k+b, saidanac k= – 4 3 , b=22 3 .radgan AB=5, MA+MB=5, amitom M aris AB da y=x wrfeebis gadakveTis wertili:Z][]\y=x,y= – 4 3 x+22 3 , saidanac x=22 7 .II xerxi. mocemuli gantoleba aviyvanoT kvadratSi.√2x 2 –14x+37 2 =(5–√2x 2 –12x+20 ) 2 ,5√2x 2 –12x+20 =x+4,kvlav kvadratSi ayvaniT miiReba: (7x–22) 2 =0, x= 22 7 .x-is es mniSvneloba mocemuli gantolebis fesvia.g) utoloba ase gadavweroT:√(x–3) 2 +1+√(x–2) 2 +4 ≤√10 .am utolobas SeiZleba aseTi geometriuli warmodgena davukavSiroT: x RerZzemdebare M(x;0) wertilidan A(3;1) da B(2;–2) wertilebamde manZilebis jami ar aRemateba√10 -s. MA+M≤AB, vpoulobT AB monakveTis sigrZes _ AB=√10 . am ori pirobidangamomdinareobs: MA+MB≤√10 . maSin M Zevs AB monakveTze _ M aris AB wrfisa dax RerZis gadakveTis wertili. AB wrfis gantolebaa y=3x-8. es wrfe x RerZs kveTswertilSi, romlis koordinatebia:y=0, x= 8 3 .II xerxi. √(x–2) 2 +4≤√10 –√(x–3) 2 +1 , (*)fesvqveSa gamosaxulebebi nebismieri x-isTvis dadebiTia. ganvixilavT x-is immniSvnelobebs, romlebisTvisac √10 ≥ √x 2 –6x+10, anu x 2 –6x≤0, x∈[0;6].(*) utolobis kvadratSi ayvaniT miviRebTx 2 –4x+8≤10–2√10(x 2 –6x+10)√10(x 2 –6x+10)≤6–x, am utolobis orive mxare arauaryofiTia (gavixsenoT, rom ganixilebax∈[0;6]). kvadratSi ayvaniT miviRebT: (3x-8) 2 ≤0saidanac x= 8 3 . cxadia, 8 3 ∈[0;6].pasuxi: 8 3 .61