I Tavi
I Tavi I Tavi
I Tavi davazustoT! roca D = 0, kvadratul gantoleba aqvs ori erTmaneTis toli amonaxseni. x 1 = x 2 = – b 2a 30 5 kvadratuli gantolebis amoxsna amocana 1 fotografiul suraTs, zomiT 12sm × 18sm, erTnairi siganis CarCo aqvs. gansazRvreT CarCos sigane, Tu misi farTobi suraTis farTobis tolia. upirveles yovlisa SevniSnoT, rom CarCoiani suraTis farTobi (ABCD marTkuTxedis farTobi) toli iqneba CarCos da suraTis farTobebis jamisa. amoxsna: vTqvaT, CarCos sigane x sm-ia, maSin CarCoiani suraTis zomebi iqneba: AB=18+2x da AD=12+2x, xolo farTobi ki – S =(18+2x)(12+2x). a.p.T. ABCD CarCos farTobi suraTis farTobis tolia, amitom vwerT gantolebas: (18 + 2x)(12 + 2x) = 2 · 12 · 18. ((18 + 2x)(12 + 2x) = 2 · 12 · 18) ⇔ (2(9 + x)2(6 + x) – 2 · 12 · 18 = 0) ⇔ |:4 ⇔ ((9 + x)(6 + x) – 2 · 3 · 18 = 0) ⇔ (x 2 + 15x + 54 – 108 = 0) ⇔ ⇔ (x 2 + 15x – 54 = 0) miviReT kvadratuli gantoleba, romlis grafikuli amoxsnac, rogorc viciT, sazogadod, gantolebis miaxloebiT amonaxsens gvaZlevs. gavecnoT kvadratuli gantolebis amoxsnis analizur xerxs. ganvixiloT ax 2 + bx + c = 0, a ≠ 0 (1) sruli kvadratuli gantoleba. (ax 2 + bx + c = 0) ⇔ |· 4a ⇔ (4a 2 x 2 + 4abx +4ac =0) ⇔ |–4ac ⇔ (4a 2 x 2 + 4abx = –4ac) ⇔ |+b 2 ⇔ (4a 2 x 2 + 4abx + b 2 = b 2 – 4ac) | tolobis marcxena mxare sruli kvadratia ⇔ ((2ax + b) 2 = b 2 – 4ac) (2) | miviReT x 2 =m saxis gantoleba. amovxsnaT: a) Tu b 2 –4ac
g) Tu b 2 – 4ac > 0, maSin ((2ax+b) 2 = b 2 – 4ac) ⇔ e.i. (1) gantolebas aqvs ori gansxvavebuli amonaxseni. fesvqveSa gamosaxulebas – (b 2 – 4ac)-s diskriminants uwodeben. igi D asoTi aRiniSneba. D = b 2 – 4ac. amrigad, ax 2 + bx + c =0, a≠0 kvadratul gantolebas, Tu: a) D>0, aqvs ori gansxvavebuli amonaxseni: x 1 = , x 2 = . (3) b) D=0 _ erTi amonaxseni: x = – b ufro zustad, ori erTmaneTis 2a . toli amonaxseni x = x = – 1 2 b 2a g) D
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g) Tu b 2 – 4ac > 0, maSin<br />
((2ax+b) 2 = b 2 – 4ac) ⇔<br />
e.i. (1) gantolebas aqvs ori gansxvavebuli amonaxseni.<br />
fesvqveSa gamosaxulebas – (b 2 – 4ac)-s diskriminants uwodeben.<br />
igi D asoTi aRiniSneba.<br />
D = b 2 – 4ac.<br />
amrigad, ax 2 + bx + c =0, a≠0 kvadratul gantolebas, Tu:<br />
a) D>0, aqvs ori gansxvavebuli amonaxseni:<br />
x 1 = , x 2 = . (3)<br />
b) D=0 _ erTi amonaxseni: x = – b ufro zustad, ori erTmaneTis<br />
2a<br />
.<br />
toli amonaxseni x = x = –<br />
1 2 b<br />
2a<br />
g) D
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