(a) Prove that 2x5 + 3y% > 5x²y³ for all positive real numbers z and y. (b) Generalise the result of (a) as follows: If a and b are non-negative integers and n =a+b, prove that az" + by" 2 na"y for all positive real numbers a and y.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 8
(a) Prove that 2x5 + 3y% > 5x²y³ for all positive real numbers z and y.
(b) Generalise the result of (a) as follows: If a and b are non-negative
integers and n =a+b, prove that
ar" + by" 2 na y
for all positive real numbers a and y.
Transcribed Image Text:Problem 8 (a) Prove that 2x5 + 3y% > 5x²y³ for all positive real numbers z and y. (b) Generalise the result of (a) as follows: If a and b are non-negative integers and n =a+b, prove that ar" + by" 2 na y for all positive real numbers a and y.
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