Question

Ajutati-ma urgent va rog!!!!

Answer 1

Răspuns:

Salut !

abcabc = 1000abc + abc = 1001abc = 7 × 143 × abc

7x × 11 × abc = 169 × 7 × 143 × abc

x = ( 169 × 7 × 143 × abc ) : ( 7 × 11 × abc ) = 169 × 3 = 2197 = 13³

= > x din proportia abcabc / 7x = 11abc / 169 este cub perfect

Succes ! : )

Answer 2

$\it \overline{abcabc}= \overline{abc000}+\overline{abc}=1000\overline{abc}+\overline{abc}=1001\overline{abc}$

Acum, proporția devine :

$\it \dfrac{1001\overline{abc}}{7x}=\dfrac{11\overline{abc}}{169}\Big|_{:\overline{abc}} \Rightarrow \dfrac{1001}{7x}=\dfrac{11}{169}\Big|_{:11} \Rightarrow \dfrac{\ 91^{(7}}{7x}=\dfrac{1}{169} \Rightarrow \dfrac{13}{x}=\dfrac{1}{169} \Rightarrow \\ \\ \\ \Rightarrow x=13\cdot169 \Rightarrow x=13\cdot13^2 \Rightarrow x=13^3\ (cub\ perfect)$