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b) Prove that 3abc ≤ a³ + b³ + c³ for nonnegative a, b, c. (Hint: In the in- equality of part (a), set w equal to the cube root of xyz.)

b) Prove that 3abc ≤ a³ + b³ + c³ for nonnegative a, b, c. (Hint: In the in- equality of part (a), set w equal to the cube root of xyz.)

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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Please do part B only.
1.31. (+) Extensions of the AGM Inequality. a) Prove that 4xyzw ≤ x² + y² + 24 + w for real numbers x, y, z, w. (Hint: Use the inequality 2tu ²+u² repeatedly.) b) Prove that 3abc ≤ a³ + b³ + c³ for nonnegative a, b, c. (Hint: In the in- equality of part (a), set w equal to the cube root of xyz.) 1:32 (1) Assuming only arithmetic (not the quadratic formula or calculus) prove
Transcribed Image Text:1.31. (+) Extensions of the AGM Inequality. a) Prove that 4xyzw ≤ x² + y² + 24 + w for real numbers x, y, z, w. (Hint: Use the inequality 2tu ²+u² repeatedly.) b) Prove that 3abc ≤ a³ + b³ + c³ for nonnegative a, b, c. (Hint: In the in- equality of part (a), set w equal to the cube root of xyz.) 1:32 (1) Assuming only arithmetic (not the quadratic formula or calculus) prove
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