Question

[Thân An Phương]

so sánh:

a) x= 9¹¹+2 / 9¹¹+3 và y= 9¹²+2 / 9¹²+3

Mình đag cần rất gấp

Answer 1

[Quỳnh Anh]

Trả lời:

\(x=\frac{9^{11}+2}{9^{11}+3}=\frac{9^{11}+3-1}{9^{11}+3}=\frac{9^{11}+3}{9^{11}+3}-\frac{1}{9^{11}+3}=1-\frac{1}{9^{11}+3}\)

\(y=\frac{9^{12}+2}{9^{12}+3}=\frac{9^{12}+3-1}{9^{12}+3}=\frac{9^{12}+3}{9^{12}+3}-\frac{1}{9^{12}+3}=1-\frac{1}{9^{12}+3}\)

Ta có: \(9^{11}< 9^{12}\)

\(\Leftrightarrow9^{11}+3< 9^{12}+3\)

\(\Leftrightarrow\frac{1}{9^{11}+3}>\frac{1}{9^{12}+3}\)

\(\Leftrightarrow-\frac{1}{9^{11}+3}< -\frac{1}{9^{12}+3}\)

\(\Leftrightarrow1-\frac{1}{9^{11}+3}< 1-\frac{1}{9^{12}+3}\)

\(\Leftrightarrow x< y\)

Vậy x < y