Question

Determinati numerele naturale a,b,pentru care a/2=b/3=c/5si 2ac+3bc-ac=423

Answer 1

$\frac{a}{2} = \frac{b}{3} = \frac{c}{5} = K$
a=2K
b=3K
c=5K
2ab+3bc-ac=423⇒ 2×2K×3K+3×3K×5K-2K×5K=423⇒12K²+45K²-10K²=423⇒47K²=423⇒K²=9⇒K=3
a=2K⇒a=2×3=6
b=3K⇒b=3×3=9
c=5K⇒c=5×3=15