A) 40
B) 45
C) 50
D) 55
Correct Answer: D
Solution :
Given, \[a+b+c+d+e=15\] \[\Rightarrow \] \[AM=1\] Now, \[GM={{\left( a\times \frac{{{b}^{2}}}{{{2}^{2}}}\times \frac{{{c}^{3}}}{{{3}^{3}}}\times \frac{{{d}^{4}}}{{{4}^{4}}}\times \frac{{{e}^{5}}}{{{5}^{5}}} \right)}^{1/15}}\] \[={{\left[ \frac{{{(120)}^{3}}\cdot 50}{{{2}^{2}}\cdot {{3}^{3}}\cdot {{4}^{4}}\cdot {{5}^{5}}} \right]}^{1/15}}=1\] \[\therefore \] \[AM=GM\] Hence, \[a=\frac{b}{2}=\frac{c}{3}=\frac{d}{4}=\frac{e}{5}\] \[\Rightarrow \,\,a=1,\,b=2,\,c=3,\,\,d=4,\,e=5\] \[\therefore \] \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+{{d}^{2}}+{{e}^{2}}\] \[={{1}^{2}}+{{2}^{2}}+{{3}^{2}}+{{4}^{2}}+{{5}^{2}}\] = 55You need to login to perform this action.
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