grandes-ecoles 2013 QIII.A.1

grandes-ecoles · France · centrale-maths1__pc Inequalities Prove or Verify an Algebraic Inequality (AM-GM, Cauchy-Schwarz, etc.)

Show that if $x$ is a real number different from 1 and from $-1$, then $x ^ { 2 } - 2 x \cos \theta + 1 > 0$ for all $\theta \in \mathbb { R }$.

Show that if $x$ is a real number different from 1 and from $-1$, then $x ^ { 2 } - 2 x \cos \theta + 1 > 0$ for all $\theta \in \mathbb { R }$.