Question

I'm asked to find the minimum value of
f(y1,y2,y3) = ( 4y1^2 + 7y2^2 + 10y3^2 ) / 4 * ( y1^2 + y2^2 + y3^2 ).
I've tried every trick up my sleeve, but can't seem to get an acceptable answer, any ideas?

Answer 1

Using abc instead of y1,y2,y3, If we take out 4(a^2 + b^2 +c^2) from the top and rewrite

as 1 + [ 3/4 *(b^2 +2c^2)/a^2 +b^2 +c^2) ] then it seems that the main case of interest is when a^2 becomes very large when the expression in [] is going to tend to 0.

So your minimum looks like 1 in that case.