Cauchy-Schwarz case for two variables

If $a^{2} + b^{2} = 1$ , and $x^{2} + y^{2} = 1$ , show that $a x + b y < 1$ .

~5 minProof · checked by AIInequalitiesCauchy-Schwarz

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.a, No. 4

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.