InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If a,b,c are non-zero real numbers, then the minimum value of the expression `((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2))` equalsA. 12B. 24C. 30D. 60 |
|
Answer» Correct Answer - C Let `P=((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2))` `(a^(4)+4+(1)/(a^(4)))(b^(2)+3+(1)/(b^(2))){(c+1)^(2)+1}` `:.a^(4)+4+(1)/(a^(4))ge6,b^(2)+3+(1)/(b^(2))ge5 " and "(c+1)^(2)+1ge 1` `[:. x+(1)/(x)ge2 " for "xgt0]` `:.P ge 6*5*1=30 implies Pge30` Hence, the required minimum value is 30. |
|