Question

A=4 la puterea n ori 3 la puterea 2n+1-2 la puterea 2n ori 9 la puterea n
Scrieti-l pe A sub forma de produs 
Verificati daca 2A este patrat perfect

Answer 1

[tex]A= 2^{2n} * 3^{2n+1} -2^{2n}*3^{2n}\\A=2^{2n}*3^{2n}(9-1) \\A=2^{2n}*3^{2n}*2^3 \\2A=2^{2n}*3^{2n}*2^4 \\ 2A=(2^{n+2}*3^{n})^2[/tex]
Care e pătrat perfect.

Answer 2

A=4^n·3^(2n+1)-2^2n·9^n
A=(2²)^n·3^2n·3-2^2n·(3²)^n
A=2^2n·3^n·3-2^2n·3^2n
A=2^2n·3^2n(3-1)
A=2^2nx3^2n·2 

2A=2·2·2^2n·3^2n=2²·6^2n este patrat perfect