Question

Acest exercitiu e cu puteri
n=( 9 la puterea 65+9 la puterea 64+ 9 la puterea 63):(7×13) este patrat perfect si cub perfect
Clasa a v.a ​

Answer 1

n = ( 9⁶⁵ + 9⁶⁴ + 9⁶³ ) : ( 7 × 13 )

( 9⁶⁵ + 9⁶⁴ + 9⁶³ ) : ( 7 × 13 ) = 9⁶³ ( 9² + 9¹ + 1 ) : 91 =

= 9⁶³ ( 81 + 9 + 1 ) : 91 = 9⁶³ × 91 : 91 = 9⁶³ × 1 = 9⁶³

9⁶³ = ( 9²¹ )³ ⇒ n cub perfect

9⁶³ = ( 3² )⁶³ = ( 3⁶³ )²  ⇒ n patrat perfect