Question

If $a_1,a_2,\dots \dots a_n$ are positive real numbers whose product is a fixed number c, then the minimum value of $a_1+a_2+\dots \dots +a_{n-1}+2a_n$ is

• A. $n(2c{)}^{\frac{1}{n}}$
• B. $(n+1)c^{\frac{1}{n}}$
• C. $2n{c}^{\frac{1}{n}}$
• D. $(n+1)(2c{)}^{\frac{1}{n}}$

Answer 1

The correct option is A $n(2c{)}^{\frac{1}{n}}$

We know that $A.M.\ge G.M.$
$L.H.S.\ge n(a_1{a}_2\dots \dots 2a_n{)}^{\frac{1}{n}}=n(2c{)}^{\frac{1}{n}}$