Mathematics - Quadratic Equation Question with Solution | TestHub

Multiplying, we get:

$xyz(1-x)(1-y)(1-z)>\frac{1}{64}..\dots \dots \dots \dots \left(1\right)$

Now, $t(1-t)=t-t^2=\frac{1}{4}-{\left(\frac{1}{2}-t\right)}^2\le \frac{1}{4}$.

So, $x(1-x)y(1-y)z(1-z)\le \frac{1}{64}$. ..............(2)

(1) and (2) are contradictory