Question

I: The real number x when added to its inverse gives the minimum positive value of the sum at x = 1
II: If product of the two positive numbers is 400, then the minimum value of their sum is 20
which of the above statements are true

• A. only I is true
• B. only II is true
• C. both I and II are true
• D. niether I nor II are true

Answer 1

Answer: (A)

only I is true

(I) $x+\frac{1}{x}=f\left(x\right)$
Use AM & GM
$\frac{x+\frac{1}{x}}{2}\ge (1{)}^{\frac{1}{2}}$
$x+\frac{1}{x}\ge 2$
(II) $xy=400$
$f\left(x\right)=x+\frac{400}{x}$
Use AM & GM
$\frac{x+\frac{400}{x}}{2}\ge (400{)}^{\frac{1}{2}}$
$x+\frac{400}{x}\ge 40$