Question

Arătați că numărul a=(3^50+3^49+3^48):13 este patrat perfect si cub perfect

Answer 1

Explicație pas cu pas:

a=(3⁵⁰+3⁴⁹+3⁴⁸):13 =>

a=3⁴⁸*(3²+3+1):13=>

a=3⁴⁸*13:13=>

a=3⁴⁸

3⁴⁸=(3²⁴)²=>a-p.p

3⁴⁸=(3¹⁶)³=>a-cub perfect

=>a e si p.p si cub perfect

Answer 2

a=(3^50+3^49+3^48):13

a=[3^48(3^2+3^1+1)]:13

a=[3^48(9+3+1)]:13

a=(3^48*13):13

a=3^48

a=3^48=(3^24)^2 => p.p.

a=3^48=(3^16)^3 => c.p.

Baftaa!