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Determinati nr naturale a,b,c pentru care [tex] \frac{a}{2}= \frac{b}{3}= \frac{c}{5} [/tex] si 2ab+3bc-ac=423

Răspuns :

Renatemambouko
a/2=b/3=c/5
2ab +3bc-ac=423
b=3a/2
c=5a/2
2a*3a/2 +3*3a/2*5a/2-a*5a/2=423
6a²/2+45a²/4-5a²/2=423
12a²+45a²-10a²=1692
47a²=1692
a²=1692:47=36
a=√36=6
b=3*a/2=3*6/2=9
c=5a/2=5*6/2=15