tm ab sao cho (2020a+b+5)(2020^a+2020a+b)=2021 27/08/2021 Bởi Piper tm ab sao cho (2020a+b+5)(2020^a+2020a+b)=2021
Đáp án: $ (a, b)\in\{(0, 42), (0, -48)\}$ Giải thích các bước giải: Ta có: $(2020a+b+5)(2020^a+2020a+b)=2021$ $\to 2020a+b+5, 2020^a+2020a+b$ lẻ Ta có: $2020a+b+5$ lẻ $\to 2020a+b$ chẵn Mà $2020^a+2020a+b$ lẻ $\to 2020^a$ lẻ $\to a=0$ $\to (2020\cdot 0+b+5)(2020^0+2020\cdot 0+b)=2021$ $\to (b+5)\cdot (1+b)=2021$ $\to 2021\quad\vdots\quad b+5$ $\to b+5\in\{43, 47, 1, 2021, -43,-46, -1, -2021\}$ $\to b\in\{39,42, -4, 2016, -48, -51, -6,-2026\}$ Thử lại $\to b\in\{42, -48\}$ $\to (a, b)\in\{(0, 42), (0, -48)\}$ Bình luận
Đáp án: $ (a, b)\in\{(0, 42), (0, -48)\}$
Giải thích các bước giải:
Ta có:
$(2020a+b+5)(2020^a+2020a+b)=2021$
$\to 2020a+b+5, 2020^a+2020a+b$ lẻ
Ta có:
$2020a+b+5$ lẻ
$\to 2020a+b$ chẵn
Mà $2020^a+2020a+b$ lẻ
$\to 2020^a$ lẻ
$\to a=0$
$\to (2020\cdot 0+b+5)(2020^0+2020\cdot 0+b)=2021$
$\to (b+5)\cdot (1+b)=2021$
$\to 2021\quad\vdots\quad b+5$
$\to b+5\in\{43, 47, 1, 2021, -43,-46, -1, -2021\}$
$\to b\in\{39,42, -4, 2016, -48, -51, -6,-2026\}$
Thử lại $\to b\in\{42, -48\}$
$\to (a, b)\in\{(0, 42), (0, -48)\}$