Statement I: For x 0 , the least value of ( x 4 + x 2 + 4 ) / x is 6. Statement II: For n positive numbers, arithmetic mean is at least geometric mean.

Question

Statement I: For x > 0 , the least value of ( x 4 + x 2 + 4 ) / x is 6. Statement II: For n positive numbers, arithmetic mean is at least geometric mean.

TestHub · Accepted Answer

Apply AM-GM (II) to six positive terms x 3 , x , 1/ x , 1/ x , 1/ x , 1/ x . Their product is 1 , so their sum ( x 4 + x 2 + 4 ) / x is at least 6, attained at x = 1 .

Mathematics - Algebra-Mixed Question with Solution | TestHub

Options:

Doubts & Discussion