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a) Prove that if n is an even integer, then n2 + 5n+2 is even. (Use a direct proof.) b) Prove that if x is an irrational number, then 5x +12 is irrational. (Use a proof by either contraposition or contradiction.)

a) Prove that if n is an even integer, then n2 + 5n+2 is even. (Use a direct proof.) b) Prove that if x is an irrational number, then 5x +12 is irrational. (Use a proof by either contraposition or contradiction.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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a) Prove that if n is an even integer, then n2 + 5n+2 is even. (Use a direct proof.) b) Prove that if x is an irrational number, then 5x +12 is irrational. (Use a proof by either contraposition or contradiction.)
Transcribed Image Text:a) Prove that if n is an even integer, then n2 + 5n+2 is even. (Use a direct proof.) b) Prove that if x is an irrational number, then 5x +12 is irrational. (Use a proof by either contraposition or contradiction.)
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