OppgaveKvadratsetningene1.2.9Regn uta) (x+2)2+(x-3)2+(x+2)(x-2)vis fasit=(x2+2·x·2+22)+(x2-2·x·3+32)+(x2-22)=(x2+4x+4)+(x2-6x+9)+(x2-4)=x2+4x+4+x2-6x+9+x2-4=3x2-2x+9 b) (4-a)(4+a)-(a+2)2+(a-2)2vis fasit=(16-a2)-(a2+4a+4)+(a2-4a+4)=16-a2-a2-4a-4+a2-4a+4=-a2-8a+16 c) -3(2-x)2-5(3x-4)2+2x2vis fasit=-3(22-2·2·x)-5((3x)2-2·3x·4+42)+2x2=-3(4-4x+x2)-5(9x2-24x+16)+2x2=-(12-12x-3x2)-(45x2-120x+80)+2x2=12+12x-3x2-45x2+120x-80+2x2=-46x2+132x-92 d) -(4-x)(4+x)-(2x-5)2-(x-13)2vis fasit=-(42-x2)-((2x)2-2·(2x)·5+52)-(x2-2·x·13+(13)2)=-(16-x2)-(4x2-20x+25)-(x2-2x3+19)=-16+x2-4x2+20x-25-x2+2x3-19=-41-4x2+20x+2x3-19=41·91·9-4x2+20x·31·3+2x3-19=3699-4x2+60x3+2x3-19=-4x2+623x-3709 e) (2-a)(2+a)-2(a+1)2-9(a-13)2vis fasit=4-a2-2(a2+2a+1)-9(a2-23a+19)=4-a2-2a2-4a-2-9a2+9·23a-9·19=4-a2-2a2-4a-2-9a2+6a-1=-12a2+2a+1 f) 2(2a-1)(2a+1)-(a-2)2-4(a+12)2vis fasit=2(4a2-1)-(a2-4a+4)-4(a2+a+14)=8a2-2-a2+4a-4-4a2-4a-1=3a2-7 g) (a-12)2+14(2a+1)2-12(2a-1)(2a+1)vis fasit=a2-a+14+14(4a2+4a+1)-12(4a2-1)=a2-a+14+a2+a+14-2a2+12=1 h) (2-1)(2+1)vis fasit=(2)2-1=2-1=1 i) (5-2)(5+2)vis fasit=(5)2-22=5-4=1 1.2.10Regn ut ved hjelp av konjugatsetningen:a) 29·31vis fasit=(30-1)(30+1)=302-12=900-1=899 b) 18·22vis fasit=(20-2)(20+2)=202-22=400-4=396 c) 25·15vis fasit=(20+5)(20-5)=202-52=400-25=375 d)103·97vis fasit=(100+3)(100-3)=1002-32=10000-9=9991 Sist faglig oppdatert 19.01.2018Skrevet av Stein Aanensen og Olav KristensenRegler for brukKopier kildehenvisningSkriv ut