Question

Answer 1

\(P\left(a\right)+2P\left(\dfrac{1}{a}\right)=a^2\)

Thay \(a=2\) ta được:

\(P\left(2\right)+2P\left(\dfrac{1}{2}\right)=4\) (1)

Thay \(a=\dfrac{1}{2}\) ta được:

\(P\left(\dfrac{1}{2}\right)+2P\left(2\right)=\dfrac{1}{4}\)

\(\Rightarrow2P\left(\dfrac{1}{2}\right)+4P\left(2\right)=\dfrac{1}{2}\) (2)

Trừ vế cho vế (2) cho (1):

\(\Rightarrow3P\left(2\right)=\dfrac{1}{2}-4=-\dfrac{7}{2}\)

\(\Rightarrow P\left(2\right)=-\dfrac{7}{6}\)