Question

Verifica daca A la 2- B la 2=cu A-B
A=10supra25
B=9supra15

Answer 1

Raspunsul e ca sunt egale.

A^2 - B^2 =
= (10/25)^2 - (9/15)^2 = (10/(5x5))^2 - (9/(3x5))^2
Aducem la numitor comun:
 ( (10x3)/(5x5x3) )^2 - ( (9x5)/(3x5x5) )^2 =
= ((10x3)^2 - (9x5)^2)  / (3x5x5)^2 =
= (900-2025) / (3x5x5)^2 =
= - 1125 / (3x5x5)^2 =
=  - (5^3 x 3^2) / (3x5x5)^2
Simplificam cu 5^2 x 3^2 si obtinem - (5 / 5^2) = - 1/5

A-B= 10/25 - 9/15
Aducem la numitor comun:
(10x3)/(5x5x3) - (9x5)/(3x5x5) = -15/(3x5x5) = - 1/5