(a) x = b, y = a
Let \(\frac{1}{X}\) = p, \(\frac{1}{y}\)= q. Then,
ap – bq = 0 ..........(i)
ab2p + a2bq = a2 + b2 \(\Rightarrow\) ab (bp + aq) = a2 + b2
\(\Rightarrow\) bp + aq = \(\frac{a^2+b^2}{ab}\) ...........(ii)
Multiplying eqn (i) by b and eqn (ii) by a, we get
abp – b2q = 0 ..........(iii)
abp + a2q = \(\frac{a^2+b^2}{b}\) .......(iv)
Now subtracting eqn (iii) from eqn (iv), we get
(a2 +b2)q = \(\frac{a^2+b^2}{b}\) \(\Rightarrow\) q = \(\frac{1}{b}\) \(\Rightarrow\) \(\frac{1}{X}\) = \(\frac{1}{b}\) \(\Rightarrow\) x = b