Question

4. Dacă a, b, c e{1,2,3,4,5,6,7,8,9}, determinați x din egalitatea:
abc+bca+cab = ab + bc+ca + x(a+b+c)​

Answer 1

Răspuns:

x=100

Explicație pas cu pas:

abc+bca+cab =ab+bc+ca+x(a+b+c)

100a+10b+c+ 100b+10c+a+ 100c+10a+b=10a+b +10b+c+ 10c+a+ x(a+b+c)

111a+111b+111c=11a+11b+11c+x(a+b+c)

111(a+b+c)=11(a+b+c)+x(a+b+c)

111(a+b+c) = (11+x)(a+b+c)

=>11+x=111

x=100