Question

Solve the following question and mark the best possible option.
Let f(a) = `(a^4 + 9)/(10a)`, then

Options

• f(a) > `4/5`

• f(a) ≥ `4/5`

• f(a) < `4/5`

• f(a) ≤ `4/5`

Answer 1

f(a) > `4/5`

We have AM ≥ GM
`(a^4 + 9)/(10a) = a^3/10 + 3/(10a) + 3/(10a) + 3/(10a) ≥ 4 root(4)(a^3/10 xx 3/(10a) xx 3/(10a) xx 3/(10a))`

⇒ `(a^4 + 9)/(10a) ≥ 2/5(2)^(1/4)`.

Since, `(27)^(1/4) > 2 ⇒ (a^4 + 9)/(10a) > 4/5`.