Question

3+6+9+.....+abc supra liniar =abc000 supra lini

Answer 1

$3+6+9+\ldots + \overline{abc}=\overline{abc00}\\3+6+9+\ldots + \overline{abc} = 100\cdot \overline{abc}\\\overline{abc}\stackrel{not}{=} x\\3+6+9+\ldots+ x=100x\\3\left(1+2+3+\ldots +\dfrac{x}{3}\right)=100x\\3\cdot \dfrac{\frac{x}{3}\left(\frac{x}{3}+1)}{2}=100x |\cdot 2\\x\left( \dfrac{x}{3}+1\right)=200x\\\dfrac{x^2}{3}+x=200 x|\cdot 3\\x^2+3x=600x\\x^2-597x=0\\x(x-597)=0\\\text{Distingem doua cazuri posibile:}\\1. x=0 (\text{nu convine})\\2.x-597=0 ,\text{ adica }x=597\\S:x=597$