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Prove that 1 1 16 ≤ (a+b+c+d) = + = + b + ax (²=²+ + + + + + + ² + 1 = 0) d for all positive numbers a, b, c, d.

Prove that 1 1 16 ≤ (a+b+c+d) = + = + b + ax (²=²+ + + + + + + ² + 1 = 0) d for all positive numbers a, b, c, d.

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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Use Cauchy-Schwarz to Prove

Prove that 16 ≤ (a + b + c + d)| for all positive numbers a, b, c, d. 1 + а b ({ / + 1 с +1) +
Transcribed Image Text:Prove that 16 ≤ (a + b + c + d)| for all positive numbers a, b, c, d. 1 + а b ({ / + 1 с +1) +
Show that the square of an average is less than or equal to the average of the squares. More precisely, show that if a₁,..., an € R, then the square of the average of a ₁,..., an is less than or equal to the average of a ₁²,...,an². 2
Transcribed Image Text:Show that the square of an average is less than or equal to the average of the squares. More precisely, show that if a₁,..., an € R, then the square of the average of a ₁,..., an is less than or equal to the average of a ₁²,...,an². 2
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