Question

Cho A= \(\dfrac{4^{15}+1}{4^{17}+1}\) và \(\dfrac{4^{12}+1}{4^{14}+1}\). So sánh A với B.

Answer 1

Ta có: \(16\cdot A=\dfrac{16\cdot\left(4^{15}+1\right)}{4^{17}+1}\)

\(\Leftrightarrow16\cdot A=\dfrac{4^{17}+16}{4^{17}+1}=1+\dfrac{15}{4^{17}+1}\)

Ta có: \(16\cdot B=\dfrac{16\cdot\left(4^{12}+1\right)}{4^{14}+1}\)

\(\Leftrightarrow16\cdot B=\dfrac{4^{14}+16}{4^{14}+1}=1+\dfrac{15}{4^{14}+1}\)

Ta có: \(4^{17}+1>4^{14}+1\)

\(\Leftrightarrow\dfrac{15}{4^{17}+1}< \dfrac{15}{4^{14}+1}\)

\(\Leftrightarrow\dfrac{15}{4^{17}+1}+1< \dfrac{15}{4^{14}+1}+1\)

\(\Leftrightarrow16A< 16B\)

hay A<B