Question

Given o(0,0) a(3,0) b(1,-1) c(3,2) then minimum value of

Answer 1

You must be knowing that arithmetic mean greater than or equal to geometric mean.

Arithmetic mean of a,b,c is a+b+c / 3

Geometric mean of a,b,c is (abc)^1/3

This implies

a+b+c / 3 >= (abc)^1/3 ....1

Now reciprocate it so we get

1/3 (1/a +1/b+ 1/c) >= (1/a×1/b×1/c)^1/3 ....2