3 Let a, b c and d be real numbers. Show that ab-cd = b(a−c)+c(b-d), and deduce that |ab − cd| ≤ |b||a – c| + |c||b − d\. - Let €, K and L be positive real numbers, and suppose that |b| < K, |c| < L, \a − c\ < €/(2K), [b−d] < €/(2L). Deduce that |ab− cd| < €.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 40E
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1.23 Let a, b c and d be real numbers. Show that ab-cd = b(a−c)+c(b−d),
and deduce that
|ab − cd| ≤ |b||a − c| + |c||b − d|.
Let E,
K and L be positive real numbers, and suppose that |b| < K,
|c| < L, \a − c] < €/(2K), |b−d| < €/(2L). Deduce that |ab − cd| < €.
-
Transcribed Image Text:1.23 Let a, b c and d be real numbers. Show that ab-cd = b(a−c)+c(b−d), and deduce that |ab − cd| ≤ |b||a − c| + |c||b − d|. Let E, K and L be positive real numbers, and suppose that |b| < K, |c| < L, \a − c] < €/(2K), |b−d| < €/(2L). Deduce that |ab − cd| < €. -
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