maTematika 7

eziume:8. mravalwevris daSla mamravlebadmoswavles unda SeeZlos mravalwevris (Tu es SesaZlebelia) warmodgena ramdenimemravalwevris namravlis saxiT. amisaTvis unda SeeZlos saerTo TanamamravlisfrCxilebs gareT gatana; wevrebis dajgufeba, Semoklebuli gamravlebis formulebisgamoyeneba.amoxsnebi, miTiTebebi:5. a) (2x+8) 2 =(2(x+4)) 2 =4(x+4) 2 .6. a) 4 12 –4 10 =4 10 (4 2 –1)=15·4 10 30;g) 27 14 –81 10 =3 42 –3 40 =3 40 (3 2 –1)=8·9 20 72;d) 6 n +6 n+1 +6 n+2 =6 n (1+6+6 2 )=43·6 n .12. d) x 2 +2x–15=0x 2 +2x+1–16=0(x+1) 2 –16=0(x+1–4)(x+1+4)=0 x=3; –5.14. a) x 2 +30x+240=x 2 +30x+225+15=(x+15) 2 +15.16. a) n 3 +11n=n(n 2 +11) cxadia, gamosaxuleba luwia, e.i. unda davamtkicoT, rom iyofa3-ze. Tu n 3-ze iyofa, winadadeba WeSmaritia, Tu n 3-ze ar iyofa, maSin misi 3-ze gayofisnaSTia 1 an 2, maSin n 2 -is naSTia 1. e.i. n 2 +11 iyofa 3-ze.b) n 4 –1=(n–1)(n+1)(n 2 +1).SevadginoT 5-ze gayofis naSTebis cxrili:n n–1 n+1 n 2 +11 02 03 04 0g) m 3 –m=m(m–1)(m+1) sami momdevno ricxvidan erTi samis jeradia, erT-erTi mainc luwia.21. ( 400 - x ) $ 80= 272, saidanac x=60.10022. 2 sT-Si auzidan gavida 300 l wyali, e.i. yovel saaTSi — 150 l. e.i. Tavidan auzSi iyo500l wyali.+ BAO = 30c25.o ⇒ ∠BOA=75°, e.i. ∠BOD=135°.AB = AOBOCAD115masc_cigni_VII_kl_cor.indd 115 03.07.2012 15:47:03