Question

Please answer this question of mine.

Answer 1

Let the cuboid has 3 sides a,b,c

then these 3 sides will satisfy the equation of Volume

that is

a,b,c will be roots of equation 8*x^3 + 12*x^2 -2*x -3

now we can form 3 equations

a+b+c = -12/8 Equation 1

ab + bc + ca = -1/4 Equation 2

a*b*c = 3/8 Equation 3

Equation 1 is negetive on RHS, which means that atleast one value of root is negetive, which means one side is negetive, which is not possible

And since Equation 3 is +ve on RHS that means 2 sides are negetive

On solving the above equation we get a,b and c as 1/2, -1/2 and -3/2

Out of these three only 1/2 is real hence it should be a cube of side 1/2