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(e) Using the inequality 2ab s a2 + b2 or otherwise, prove that b2 ab s ca2 + 4c for all positive numbers a, b and c. (b) It is known that x2 + y? 2 2xy for all real numbers x, y (Do not prove this). (i) Show that x² + y? + z² > xy + xz + yz (ii) Hence deduce (x +y + z)² > 3(xy + xz + yz)

(e) Using the inequality 2ab s a2 + b2 or otherwise, prove that b2 ab s ca2 + 4c for all positive numbers a, b and c. (b) It is known that x2 + y? 2 2xy for all real numbers x, y (Do not prove this). (i) Show that x² + y? + z² > xy + xz + yz (ii) Hence deduce (x +y + z)² > 3(xy + xz + yz)

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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(e) Using the inequality 2ab sa² + b2 or otherwise, prove that b2 ab < ca2 +- 4c for all positive numbers a, b and c. (b) It is known that x2 + y? 2 2xy for all real numbers x, y (Do not prove this). (i) Show that x2 + y? + z² > xy + xz + yz (ii) Hence deduce (x +y +z)² > 3(xy + xz + yz)
Transcribed Image Text:(e) Using the inequality 2ab sa² + b2 or otherwise, prove that b2 ab < ca2 +- 4c for all positive numbers a, b and c. (b) It is known that x2 + y? 2 2xy for all real numbers x, y (Do not prove this). (i) Show that x2 + y? + z² > xy + xz + yz (ii) Hence deduce (x +y +z)² > 3(xy + xz + yz)
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