Aflati numerele naturale a,b,c ,care satisfac conditiile : a supra 11 = b supra 6, b supra 4=c supra 663 stiind ca 55a+65b-c=1

a/11=b/6 a=11b/6 a=(11× 4c/663)/6=22c/1989
b/4=c/663 b=4c/663
55a+65b-c=1
55×22c/1989 +65×4c/663-c=1
1210c +780c-1989c=1989
c =1989
a=(22×1989)/1989=22
b=4×1989)/663=12

a=22
b=12
c=1989

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Аноним Аноним · Answer 2 · 2016-03-26T22:19:24+02:00

a= ? , b= ? , c= ?   _a_ =_b_ 6a= 11b b=_6a_
______________ 11 6 11
_a_= _b_
11 6
_b_ = _4c_ 663b=4c b=_4c_
_b_ = _c_ 4 663 663
4 663
b= b
55a+ 65b- c= 1
_6a_ = _4c_
11 663

6a·663=4·11cI: 4

663a=11c

a=_11c_
663

55·_11c_ + 65·_4c_ - c = 1
663 663

55·11c+ 65·4c - 663c= 663

605c+ 260c - 663c= 663

865c - 663c=663

202c=663

c=_663_
202

  _663_
a=_11· 202 _ a=_11·663_ : 663 a=_11·663·_1_
663 202 202 663

a=_11_
202
_663_
b=_4· 202 __ b=_4·663_ : 663 b=_4·663·_1_
  663 202 202    663

b=_4_
202

b=_2_
101

probă: 55·_11_ + 65·_2_ - _663_ = 1
202 101 202

605+ 260- 663= 202
202=202