A) \[a({{b}^{2}}+{{a}^{2}})=c({{b}^{2}}+{{c}^{2}})\]
B) \[a({{b}^{2}}+{{c}^{2}})=c({{a}^{2}}+{{b}^{2}})\]
C) \[{{a}^{2}}(b+c)={{c}^{2}}(a+b)\]
D) None of these
Correct Answer: B
Solution :
If \[a,\ b,\ c\] are in G.P. Then \[{{b}^{2}}=ac\] \[\Rightarrow \] \[{{b}^{2}}(a-c)=ac(a-c)\]\[\Rightarrow \]\[{{b}^{2}}a-{{b}^{2}}c={{a}^{2}}c-a{{c}^{2}}\] \[\Rightarrow \] \[a({{b}^{2}}+{{c}^{2}})=c({{a}^{2}}+{{b}^{2}})\]. Trick: Put \[a=1,\ b=2,\ c=4\] and check the alternates.
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