Problem
ALG-B2-M03-P001 Two pairs
#1
★★☆☆☆ Level 2 of 5
Prove that \((a^2+b^2)(c^2+d^2)\ge(ac+bd)^2\).
Hint 1. This is the standard Cauchy form.
Hint 2. You may expand and get a square.
By Cauchy for \((a,b)\) and \((c,d)\), \((a^2+b^2)(c^2+d^2)\ge(ac+bd)^2\). After expansion, the difference is \((ad-bc)^2\ge0\).
Cauchy-Schwarz module training problem. Method tags: cauchy, standard-form.