A) 18
B) 16
C) 14
D) None of these
Correct Answer: A
Solution :
Let three number of G.P. i.e., \[a,\,ar,\,a{{r}^{2}}\] \[a+ar+a{{r}^{2}}=38\] and \[{{a}^{3}}{{r}^{3}}=1728\] ?..(i) \[a(1+r+{{r}^{2}})=38\] ?..(ii) From equation (i) \[ar=12\] Þ \[a=\frac{12}{r}\] From equation (ii) \[\frac{12}{r}(1+r+{{r}^{2}})=38\] on solving \[r=2/3\] and \[a=\frac{12\times 3}{2}=18\] Required number 18, 12, 8 Maximum number i.e., 18.
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