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E\L-LOVELY-H\math21-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12 VIIth 11-5-13
bdkbZ lkjf.kd % izdkj ,oa xq.k&/eZ
uksV
4 − 2 4 2
mnkgj.kkFkZµ 4 5
− 3 5 5 − 3
4 " 8 % 5 5 8 5 4 / 5 & 4 "
r`rh; dksfV
osQ lkjf.kd dk foLrkj
eku yks r`rh; dksfV dk lkjf.kd gSµ
a 1 b 1 c 1
4 a 2 b 2 c 2
a 3 b 3 c 3
lkjf.kd dk foLrkj lk/kj.kr;k igyh iafDr osQ vo;oksa osQ lkis{k vFkok igys LrEHk
osQ
vo;oksa osQ lkis{k fd;k tkrk gSA
igyh iafDr osQ vo;oksa ( ) osQ lkis{k foLrkj #$!
*
1
5
dYiuk djks fd ∆ 4 5
3
tgk¡ 7
7
Øe'k% lkjf.kdksa dks izdV djrs gSaA
uksVµ foLrkj esa inksa osQ fpÉ Øe'k% Øe esa ysrs gSaA
7
7
dks fuEufyf[kr fof/ }kjk Kkr djrs gSaµ
4 ftl iafDr rFkk LrEHk esa vkrk gS mUgsa NksM+us ij izkIr lkjf.kd
4 ftl iafDr rFkk LrEHk esa vkrk gS mUgsa NksM+us ij izkIr lkjf.kd
4 ftl iafDr rFkk LrEHk esa vkrk gS mUgsa NksM+us ij izkIr lkjf.kd
;gk¡] igyh iafDr rFkk igys LrEHk esa vkrk gS_ vr% bUgsa NksM+us ij izkIr lkjf.kd
b c
9 9 4 2 2
b 3 c 3
blh izdkj] igyh iafDr rFkk nwljs LrEHk esa vkrk gS] vr% bUgsa NksM+us ij izkIr lkjf.kd
a b
9
9 4 2 2
a 3 b 3
rFkk igyh iafDr rFkk rhljs LrEHk esa vkrk gS] vr% bUgsa NksM+us ij izkIr lkjf.kd
a b
9
9 4 2 2
a 3 b 3
lehdj.k (1) ls] fn;s gq, lkjf.kd dk foLrkj djus ij ikrs gSaµ
b c a c a b
4 b 2 3 c 2 3 − b = 1 a 2 3 c 2 3 + c = 1 a 2 3 b 2 3
5 5 5 3 5
5 5 5 3 5