Question

Arătați ca nr a=17+17x2+17x3+.....+17x17 este pătrat perfect

Answer 1

[tex]a=17+17*2+17*3+...+17*17 \\ \Leftrightarrow a=17(1+2+3+...+17) \\ \Leftrightarrow a=17* \frac{17*18}{2} \\ \Leftrightarrow a=17*17*9\\ \Leftrightarrow a=17^{2}*3^{2}[/tex]

[tex]Se\ stie\ din\ teorie\ ca\ produsul\ oricaror\ 2\ patrate\ perfecte\ este\\ un\ patrat\ perfect.[/tex]

Answer 2

a=17+17x2+17x3+.....+17x17 =
=17(1+2+3+.....+17) =
=17×17×(17+1)/2=
=17²×18/2=
=17²×9=
=17²×3²=
=(17×3)²=
=51²