Câu hỏi của Nguyễn Lê Trà My

Question

Bài 1 :Cho a = 2 mũ 1 +2 mũ 2 + 2 mũ 3 +.... + 2 mũ 100 .Tìm x thuộc N sao cho a+2=2 mũ x

Bài 2 : Có hay không 3 số tự nhiên lẻ a,b,c thỏa mãn a mũ 2 + b mũ 2 - c mũ 2 = 2016

...

Jennie Kim · Accepted Answer

$a=2^1+2^2+2^3+...+2^{100}$

$2a=2^2+2^3+2^4+...+2^{101}$

$2a-a=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2^1+2^2+2^3+...+2^{100}\right)$

$a=2^{101}-2$

$a+2=2^{101}-2+2=2^{201}$

$\Rightarrow x=101$

Câu trả lời:

$a=2^1+2^2+2^3+...+2^{100}$

$2a=2^2+2^3+2^4+...+2^{101}$

$2a-a=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2^1+2^2+2^3+...+2^{100}\right)$

$a=2^{101}-2$

$a+2=2^{101}-2+2=2^{201}$

$\Rightarrow x=101$

Tran Thi Thu Hien · Answer

$a=2^1+2^2+2^3+...+2^{100}$

$2a=2^2+2^3+2^4+...+2^{99}+2^{100}$

$2a-a=\left(2^2+2^3+2^4+...+2^{99}+2^{100}\right)-\left(2^1+2^2+2^3+...+2^{100}\right)$

$a=2^{99}-2$

$a+2=2^{99}-2+2=2^{99}$

$\Rightarrow x=99$

Câu trả lời:

$a=2^1+2^2+2^3+...+2^{100}$

$2a=2^2+2^3+2^4+...+2^{99}+2^{100}$

$2a-a=\left(2^2+2^3+2^4+...+2^{99}+2^{100}\right)-\left(2^1+2^2+2^3+...+2^{100}\right)$

$a=2^{99}-2$

$a+2=2^{99}-2+2=2^{99}$

$\Rightarrow x=99$