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Prove that the product xy of two real numbers x and y is nonnegative if if and only if the absolute value Ixtyl of their sum is the sum 1x1 + ly! of their absolute values.

Prove that the product xy of two real numbers x and y is nonnegative if if and only if the absolute value Ixtyl of their sum is the sum 1x1 + ly! of their absolute values.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove that the product xy of two real numbers is nonnegative if and only if the absolute x and y value Ixty of their sum is the sum 1x1 + ly! of their absolute values. (-) Recall that 1x1 = x iff x>=0. (<-) Show ab<0 leads to a contradiction. Then assume ab >=0. Prove by cases: (i) Let ab=0. (ii) Let ab > 0.
Transcribed Image Text:Prove that the product xy of two real numbers is nonnegative if and only if the absolute x and y value Ixty of their sum is the sum 1x1 + ly! of their absolute values. (-) Recall that 1x1 = x iff x>=0. (<-) Show ab<0 leads to a contradiction. Then assume ab >=0. Prove by cases: (i) Let ab=0. (ii) Let ab > 0.
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