A) (6 and 16)
B) (6 and 60)
C) (5 and 125)
D) (8 and 216)
Correct Answer: C
Solution :
(c): Let the two number be ?a? and ?b? Then, \[HM=\frac{2ab}{a+b}\] and \[GM=\sqrt{ab}\] Putting the value of HM and GM in the above relation, we get, \[\frac{125}{13}=\frac{2ab}{a+b}\] and \[25=\sqrt{ab}\] \[\Rightarrow \]\[ab=625\] \[\Rightarrow \]\[\frac{2\times 625}{a+b}=\frac{125}{13}\] \[\Rightarrow \]\[a+b=130;\] Also, \[{{(a-b)}^{2}}={{(a+b)}^{2}}-4ab\] \[\Rightarrow \]\[{{(a-b)}^{2}}=16900-2500\] \[\Rightarrow \]\[a-b=\sqrt{14400}=120\] So, \[a+b=130;a-b=120\] \[\Rightarrow \]\[a=125;b=5\]
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