PROBLEM/SITUATION: 1.) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute value |x +y| of their sum is the sum |x| + |y| of their absolute values.
(NFQ1)
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PROBLEM/SITUATION:
1.) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute value |x +y| of their sum is the sum |x| + |y| of their absolute values.
For no.1:
Recall that |x| = 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
NOTE: Type only your answers. Please do not handwritten your answers. Make sure your formulas, solutions and answers' format are all correct.

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