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ab-cd

Source:

March 23, 2008
trigonometrycomplex numbers

Problem Statement

Suppose that a,b,c,d a, b, c, d are real numbers satisfying a≥b≥c≥d≥0 a \geq b \geq c \geq d \geq 0, a^2 \plus{} d^2 \equal{} 1, b^2 \plus{} c^2 \equal{} 1, and ac \plus{} bd \equal{} 1/3. Find the value of ab \minus{} cd.
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