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

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