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 :
The given equation is \[pq{{x}^{2}}-{{(p+q)}^{2}}x+{{(p+q)}^{2}}=0\] \[x=\frac{{{(p+q)}^{2}}\pm \sqrt{{{(p+q)}^{4}}-4pq{{(p+q)}^{2}}}}{2pq}\] \[x=\frac{{{(p+q)}^{2}}\pm ({{p}^{2}}-{{q}^{2}})}{2pq}\] Now, taking + sign \[x=\frac{p+q}{q}\] and taking - sign \[x=\frac{p+q}{p}\] \[\therefore \]Solution set is \[\left\{ \frac{p+q}{p},\frac{p+q}{q} \right\}\].
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