# Cauchy Schwartz Inequality: Minimum Variables

Cauchy Schwartz Inequality stems from the simple looking beautiful identity.

$(a^2 + b^2)(c^2 + d^2) = (ac – bd)^2 + (ad + bc)^2$.

Now, using the trivial inequality that $x^2 \geq 0$, we get $(a^2 + b^2)(c^2 + d^2) \geq (ad + bc)^2$, when the equality holds if ad = bc rather $\frac{a}{c} = \frac{b}{d}$.

This is the basis of Cauchy Schwartz Inequality. Similarly, it can be generalized to higher dimensions.

$(a^2+b^2+c^2)(d^2+e^2+f^2)≥(ad+be+cf)^2$. and equality holds iff $\frac{a}{d} = \frac{b}{e} = \frac{c}{f}$.