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Lemma 1: if x, y ≤R and x > 0 and y < 0 then xy < 0. Lemma 2: if x, y ER and x < 0 and y < 0 then ry > 0. Lemma 3: if x > 0 then 1/x > 0. Lemma 4: if x < 0 then 1/x < 0. Using the above lemmas prove that ab <0 implies either (i) a>0 and b <0 or (ii) a <0 and b > 0.

Lemma 1: if x, y ≤R and x > 0 and y < 0 then xy < 0. Lemma 2: if x, y ER and x < 0 and y < 0 then ry > 0. Lemma 3: if x > 0 then 1/x > 0. Lemma 4: if x < 0 then 1/x < 0. Using the above lemmas prove that ab <0 implies either (i) a>0 and b <0 or (ii) a <0 and b > 0.

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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Lemma 1: if x, y ≤R and x > 0 and y < 0 then xy < 0. Lemma 2: if x, y ER and x < 0 and y < 0 then ry > 0. Lemma 3: if x > 0 then 1/x > 0. Lemma 4: if x < 0 then 1/x < 0. Using the above lemmas prove that ab <0 implies either (i) a>0 and b <0 or (ii) a <0 and b > 0.
Transcribed Image Text:Lemma 1: if x, y ≤R and x > 0 and y < 0 then xy < 0. Lemma 2: if x, y ER and x < 0 and y < 0 then ry > 0. Lemma 3: if x > 0 then 1/x > 0. Lemma 4: if x < 0 then 1/x < 0. Using the above lemmas prove that ab <0 implies either (i) a>0 and b <0 or (ii) a <0 and b > 0.
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