A) 32
B) 16
C) 23
D) \[-\,23\]
Correct Answer: C
Solution :
[c] \[{{a}^{2}}+{{b}^{2}}=5ab\] \[\Rightarrow \,\,\,\frac{{{a}^{2}}+{{b}^{2}}}{ab}=5\] \[\Rightarrow \,\,\,\frac{a}{b}+\frac{b}{a}=5\] On squaring both sides. \[\therefore \,\,\,{{\left( \frac{a}{b}+\frac{b}{a} \right)}^{2}}=25\] \[\Rightarrow \,\,\,\frac{{{a}^{2}}}{{{b}^{2}}}+\frac{{{b}^{2}}}{{{a}^{2}}}+2=25\] \[\Rightarrow \,\,\,\frac{{{a}^{2}}}{{{b}^{2}}}+\frac{{{b}^{2}}}{{{a}^{2}}}=25-\,2=23\].
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