Question

Va rog mult sa ma ajutați dau coroana ​

Answer 1

Răspuns:

$\bf A=\green{2^{2n+2} \cdot 5^{2n+2}}\cdot 3- 2^{2n+3}\cdot 5^{2n+2}$

$\bf A= 2^{2n+2} \cdot 5^{2n+2}\cdot\Big[ 2^{2n+2-(2n+2)} \cdot 5^{2n+2-(2n+2)}\cdot 3 -2^{2n+3-(2n+2)} \cdot 5^{2n+2-(2n+2)}\Big]$

$\bf A=2^{2n+2} \cdot 5^{2n+2}\cdot\Big[2^{2n+2-2n-2} \cdot 5^{2n+2-2n-2}\cdot3 -2^{2n+3-2n-2} \cdot 5^{2n+2-2n-2}\Big]$

$\bf A=2^{2n+2} \cdot5^{2n+2}\cdot\Big[2^{0} \cdot 5^{0}\cdot3 -2^{1} \cdot 5^{0}\Big]$

$\bf A=2^{2n+2} \cdot 5^{2n+2}\cdot\big(1 \cdot1\cdot3 -2 \cdot 1\big)$

$\bf A=2^{2n+2} \cdot 5^{2n+2}\cdot\big(3 -2\big)$

$\bf A=2^{2n+2} \cdot 5^{2n+2}\cdot1$

$\bf A=2^{2\cdot(n+1)} \cdot 5^{2\cdot(n+1)}$

$\bf A=\big(2 \cdot 5\big)^{2\cdot(n+1)}$

$\bf A=\Big[\big(2 \cdot5\big)^{n+1}\Big]^{2}$

$\red{\boxed{\bf A=\Big(10^{n+1}\Big)^{2}\implies patrat ~perfect~}}$