Question

If $a,b,c,d$ are four positive real numbers such that $abcd=1$ then least value of $(a+4)(b+4)(c+4)(d+4)$ is

• A. $16$
• B. $125$
• C. $25$
• D. $625$

Answer 1

Answer: (A)

$16$

Solution:

If $abcd=1$. Then, to find the minimum value of $(a+4)(b+4)(c+4)(d+4)$, one way is to use the fact that Arithmetic Mean of positive numbers is always greater than or equal to their Geometric Mean.

The other way is to assume $a=b=c=d=4$.

Then we get the minimum value to be $16$.