Question

arata ca numarul: 5x ( 3^2002-3^2001-9^1000) este patrat perfect

Answer 1

Răspuns:

$5 \times ( {3}^{2002} - {3}^{2001} - {9}^{1000} ) = \\ 5 \times [ {3}^{2002} - {3}^{2001} - ( {3}^{2} ) ^{1000} ] = \\ 5 \times ( {3}^{2002} - {3}^{2001} - {3}^{2000} ) = \\ 5 \times {3}^{2000} \times ( {3}^{2} - 3 - 1) = \\ 5 \times {3}^{2000} \times 5 = \\ {3}^{2000} \times {5}^{2} = \\ ( {3}^{1000} \times 5) ^{2} \: \: \: \: \: -> patrat \: \: perfect$

sper că te-am ajutat!

Answer 2

Răspuns:

Explicație pas cu pas:

5(3²⁰⁰²-3²⁰⁰¹-9¹⁰⁰⁰)=5[3²⁰⁰²-3²⁰⁰¹-(3²)¹⁰⁰⁰]=5(3²⁰⁰²-3²⁰⁰¹-3²⁰⁰⁰)=5×3²⁰⁰⁰(3²-3-1)=5×3²⁰⁰⁰×5=3²⁰⁰⁰×5²=(3¹⁰⁰⁰×5)² => pp