Câu hỏi của Hoàng Phương Linh

Question

so sánh A và B

A=1990¹⁰+1 / 1990¹¹+1

B=1990¹¹+1 / 1990¹²+1

Wall HaiAnh · Accepted Answer

$A=\frac{1990^{10}+1}{1990^{11}+1};B=\frac{1990^{11}+1}{1990^{12}+1}$

Ta có:

$A=\frac{10\cdot\left(1990^{10}+1\right)}{10\cdot\left(1990^{11}+1\right)}$

$\Rightarrow A=\frac{1990^{11}+10}{1990^{12}+10}$

$\Rightarrow A=\frac{1990^{11}+1+9}{1990^{12}+1+9}$

$\Rightarrow A< B$

Câu trả lời:

$A=\frac{1990^{10}+1}{1990^{11}+1};B=\frac{1990^{11}+1}{1990^{12}+1}$

Ta có:

$A=\frac{10\cdot\left(1990^{10}+1\right)}{10\cdot\left(1990^{11}+1\right)}$

$\Rightarrow A=\frac{1990^{11}+10}{1990^{12}+10}$

$\Rightarrow A=\frac{1990^{11}+1+9}{1990^{12}+1+9}$

$\Rightarrow A< B$