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If a, b, c, d and p are distinct real numbers such that (a² + b² + c²)p² -2(ab + bc + cd)p+ (b²+ c² + ²) ≤0, then prove that a, b, c, d are in G.P.

If a, b, c, d and p are distinct real numbers such that (a² + b² + c²)p² -2(ab + bc + cd)p+ (b²+ c² + ²) ≤0, then prove that a, b, c, d are in G.P.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter0: A Review Of Basic Algebra
Section0.1: Sets Of Real Numbers
Problem 42E
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ILLUSTRATION 5.36 If a, b, c, d and p are distinct real numbers such that (a² + b² + c²p²-2(ab + bc + cd)p+ (b² + ² + d²) ≤0, then prove that a, b, c, d are in G.P. Find four numbers in G.P. whose sum is 85 and product is 4096.
Transcribed Image Text:ILLUSTRATION 5.36 If a, b, c, d and p are distinct real numbers such that (a² + b² + c²p²-2(ab + bc + cd)p+ (b² + ² + d²) ≤0, then prove that a, b, c, d are in G.P. Find four numbers in G.P. whose sum is 85 and product is 4096.
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