A) 1
B) 2
C) 3
D) 4
Correct Answer: D
Solution :
If \[a,\ b,\ c\] are in A.P. \[\Rightarrow \]\[2b=a+c\] So, \[\frac{{{(a-c)}^{2}}}{({{b}^{2}}-ac)}=\frac{{{(a-c)}^{2}}}{\left\{ {{\left( \frac{a+c}{2} \right)}^{2}}-ac \right\}}\] \[=\frac{{{(a-c)}^{2}}4}{[{{a}^{2}}+{{c}^{2}}+2ac-4ac]}=\frac{4{{(a-c)}^{2}}}{{{(a-c)}^{2}}}=4\]. Trick: Put\[a=1,\ b=2,\ c=3\], then the required value is\[\frac{4}{1}=4\].You need to login to perform this action.
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