I recently appeared nmtc final round junior and these are the questions in which i have doubt. Please upload the solution if you know the answer

** Q.1** a,b,c are positive real numbers. Find the minimum value of
\( \frac{a+3c}{a+2b+c} \)+ \( \frac{4b}{a+b+2c} \)- \( \frac{8c}{a+b+3c} \)
I got the answer \( \frac{2}{5} \) . Is it correct?

** Q.2** show that for any natural number n, there is a positive integer all of whose digits are 5 or 0 and is divisible by n. I have totally no idea how this one is done , and i ended up just bluffing some answer in the end.
thanks in advance for the solution

## Comments

Sort by:

TopNewestQuestion 1: The minimum value is \(12\sqrt2 - 17\) and it occurs when \((a,b,c) = \left( \dfrac32 - \sqrt2, \dfrac1{\sqrt2} - \dfrac12 , \dfrac1{\sqrt2} \right) \). – Pi Han Goh · 1 month, 1 week ago

Log in to reply

– Sayantan Dhar · 1 month, 1 week ago

can you please post the detailed solutionLog in to reply