correct answer is: c) 6
formula use: (a-b)² = a² – 2.a.b + b²

Explanation

\frac{a}{b}\ =\ \frac{b}{a}\ –\ 2
\rightarrow\ \frac{a}{b}\ -\ \frac{b}{a}\ =\ -2
\rightarrow\ \frac{a^2\ -\ b^2}{ab}\ =\ -2 _[L.C.M]
\rightarrow\ \left(\frac{a^2\ -\ b^2}{ab}\right)^2\ =\ \left(-2\right)^2 _{[add square in both side]}
\rightarrow\ \frac{\left(a^2\ -\ b^2\right)^2}{\left(ab\right)^2}\ =\ 4
\rightarrow\ \frac{\left(a^2\right)^2\ -\ 2.a^2.\ b^2\ +\ \left(b^2\right)^2}{\left(ab\right)\left(ab\right)}\ =\ 4
\rightarrow\ \frac{a^4\ -\ 2.a^2.b^2\ +\ b^4}{a^2b^2}\ =\ 4
\rightarrow\ a^4\ -\ 2.\ a^2.\ b^2\ +\ b^4\ =\ 4a^2b^2 _{[cross multiply]}
\rightarrow\ a^4\ +\ b^4\ =\ 4a^2b^2\ +\ 2a^2b^2
\rightarrow\ a^4\ +\ b^4\ =\ 6a^2b^2
\therefore\ a^4\ +\ b^4\ =\ 6a^2b^2

Now,
\frac{a^2}{b^2}\ +\ \frac{b^2}{a^2}
\rightarrow\ \frac{a^4\ +\ b^4}{a^2b^2} _[L.C.M]
\rightarrow\ \frac{6a^2b^2}{a^2b^2} _{[ put the value of a⁴ + b⁴]}
\rightarrow\ 6
Ans: \frac{a^2}{b^2}\ +\ \frac{b^2}{a^2}\ =\ 6.