>>164914716I have worked through this problem, and there is no solution
Let's define our variables:
a = apple
b = banana
c = pineapple
Then we reassign new variables from the old ones, each one is linearly independent
A = b+c
B = c+a
C = a+b
then reverse solving:
a = (C - A + B)/2
b = (A - B + C)/2
c = (B - C + A)/2
plugging this in, we get a new equation:
8 = [(A+B)C^2 + (A+C)B^2 + (B+C)A^2 - 3*ABC]/(ABC)
which reduces to:
5 = [(A+B)C^2 + (A+C)B^2 + (B+C)A^2]/(ABC)
Now what? Well let's start with A, B, C = 1. In this case, the right hand side = 6.
Now we show that, for any value of A, B, C, adding 1 to that value will cause the right hand side to be greater than it was before.
Since this is the case, and the minimum value is 6, there is no way we can ever get it down to a 5. Therefore this problem has no solution
