Question

Verificat:
a)3la puterea 1•3la puterea a 2•3la puterea a 3•....•3la puterea 100+(81 la puterea a 2)totul la 631=10•9la puterea 2524

Answer 1

a)3¹•3²•3³•....•3¹⁰⁰+(81²)⁶³¹=10•9²⁵²⁴

1+2+3+...+100=100*101/2=5050

(81²)⁶³¹= (3⁴*²)⁶³¹=3⁸*⁶³¹=3⁵⁰⁴⁸

deci avem :

3¹•3²•3³•....•3¹⁰⁰+(81²)⁶³¹= 3⁵⁰⁵⁰+3⁵⁰⁴⁸= 3⁵⁰⁴⁸*(3²+1)= 3⁵⁰⁴⁸*10=
= (3²)²⁵²⁴*10= 9²⁵²⁴*10


Deci egalitatea este adevarata.