柯西不等式

Success

$(a^{2} + b^{2}) (c^{2} + d^{2}) \geq (a c + b d)^{2}$
$(a_{1}^{2} + a_{2}^{2} + a_{3}^{2}) (b_{1}^{2} + b_{2}^{2} + b_{3}^{2}) \geq (a_{1} b_{1} + a_{2} b_{2} + a_{3} b_{3})^{2}$