A) \[\left\{ \frac{p}{q},\,\frac{q}{p} \right\}\]
B) \[\left\{ pq,\,\frac{p}{q} \right\}\]
C) \[\left\{ \frac{q}{p},\,pq \right\}\]
D) \[\left\{ \frac{p+q}{p},\,\frac{p+q}{q} \right\}\]
E) \[\left\{ \frac{p-q}{p},\,\frac{p-q}{q} \right\}\]
Correct Answer: D
Solution :
Given equation \[(pq)\,{{x}^{2}}-{{(p+q)}^{2}}x+{{(p+q)}^{2}}=0\] Let solution set is \[\left\{ \frac{p+q}{p},\,\frac{p+q}{q} \right\}\] Sum of roots = \[\frac{{{(p+q)}^{2}}}{pq}\] Þ \[\frac{p+q}{p}+\frac{p+q}{q}=\frac{{{(p+q)}^{2}}}{pq}\] Similarly, product of roots = \[\frac{{{(p+q)}^{2}}}{pq}\] Þ \[\frac{p+q}{p}\times \frac{p+q}{q}=\frac{{{(p+q)}^{2}}}{pq}\].
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