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Determinati a+b+ca știind ca: abc+bca+cab=222

Răspuns :

abc + bca + cab = 222

100a + 10b + c + 100b + 10c + a + 100c + 10a + b = 222

111a + 111b + 111 c = 222

111(a + b + c) = 222

a + b + c = 2
abc+bca+cab=222

(100×a+10×b+c)+(100×b+10×c+a)+(100×c+10×a+b)=222

(100×a+a+10×a)+(10×b+100×b+b)+(c+10×c+100×c)=222

111×a+111×b+111×c=222

a+b+c=222:111

a+b+c=2