# Roots' relation

Algebra Level 2

Suppose $$m$$ and $$n$$ are real numbers such that the roots of the equation $$2x^2-mx+8=0$$ are $$\alpha$$ and $$\beta$$ while the roots of the equation $$5x^2-10x+5n=0$$ are $$\dfrac{1}{\alpha}$$ and $$\dfrac{1}{\beta}$$.

Find the value of $$mn$$.

×