მასწავლებლის წიგნი

17 I xerxi. mocemuli gantoleba ase gadavweroT:√(x–1) 2 +4+√(x–8) 2 +25≤7√2 . movZebnoT abscisaTaRerZze iseTi A(x; 0) wertili, romlidanac B(1; ±2)da C(8; ±5) wertilebamde manZilebis jamia 7√2 . Bda C wertilebis ordinatebis niSani calsaxad araagansazRvruli, radgan CvenTvis maTi kvadratebiacnobili. Tumca, (1; 2) da (1; –2), agreTve (8; 5) da(8; –5) wertilebi OX RerZis mimarT simetriulia daamitom am RerZis nebismieri wertilidan erTi daimave manZilebiTaa daSorebuli.ganvixiloT B(1; 2) da C(8;–5) SemTxveva; maSinAB=√(x–1) 2 +4, AC=√(x–8) 2 +25, BC=√7 2 +7 2 =7√2 .pirobiT, AB+AC=BC, rac niSnavs, rom A wertiliBC monakveTs ekuTvnis. vTqvaT,y=kx+baris BC wrfis gantoleba.maSin Z ] 2=k+b[] –5=8k+b, saidanac k=–1, b=3.\BC wrfis gantolebaa y=–x+3.am wrfis OX RerZTan gadakveTis wertilia (3; 0). maSasadame, x=3.II xerxi.√ x 2 –2x+5 +√x 2 –16x+89 =7√2 .es gantoleba ase gadavweroT:√x 2 –16x+89 =7√2 –√ x 2 –2x+5 .tolobis orive mxare aviyvanoT kvadratSi.x 2 –16x+89=98–14⋅√2 ⋅√ x 2 –2x+5 +x 2 –2x+5–14x–14=–14 √ 2x 2 –4x+10x+1=√ 2x 2 –4x+10 .Tu x+1³0, maSinx 2 +2x+1=2x 2 –4x+10x 2 –6x+9=0(x–3) 2 =0x=3cvladis es mniSvneloba akmayofilebs yvela pirobas.pasuxi: x=3.62