Câu hỏi của Love Aikatsu

Question

Cho A=2²+2³+...+2⁶⁰

Chứng minh A chia hết cho 3

Tìm x,y thuộc N biết:

(41-2.x).(2.y-7)=21

Darlingg🥝 · Accepted Answer

$A=2^2+2^3+.......2^{60}$

$A=\left(2+2^2\right)+\left(2^3+2^4\right)+\left(2^5+2^6\right)+........\left(2^{59}+2^{60}\right)$

$A=2.\left(1+2\right)+2^3.\left(1+2\right)+......2^{59}.\left(1+2\right)$

$A=2.3+2^3.3+....2^{59}.3$

$A=3.\left(2+2^3+...2^{59}\right)$

$\Rightarrow A⋮3$
$\text{Tìm x,y thuộc N biết: (41-2.x).(2.y-7)=21}$

$\left(41-2.x\right)=21$

$\Rightarrow2.x=41-21$

$\Rightarrow2.x=20$

$\Rightarrow x=20:2$

$\Rightarrow x=10$

$2.y-7=21$

$\Rightarrow2.y=21+7$

$\Rightarrow2.y=28$

$\Rightarrow y=28:2$

$\Rightarrow y=16$

Vậy x = 10 y =16

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