3.46. Given below is a proof of a result. What is the result? Proof Assume, without loss of generality, that x and y are even. Then x = 2a and y = 2b for integers a an b. Therefore, xy + xz+ yz = (2a) (26) + (2a) z+ (2b) z = 2 (2ab +az + bz) . Since 2ab + az + bz is an integer, ry +xz+yz is even.
3.46. Given below is a proof of a result. What is the result? Proof Assume, without loss of generality, that x and y are even. Then x = 2a and y = 2b for integers a an b. Therefore, xy + xz+ yz = (2a) (26) + (2a) z+ (2b) z = 2 (2ab +az + bz) . Since 2ab + az + bz is an integer, ry +xz+yz is even.
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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Given below is a proof of a result. What is the result?
Proof Assume, without loss of generality, that xx and yy are even. Then x=2ax=2a and y=2by=2b for integers aa and b.b. Therefore,
xy+xz+yz=(2a)(2b)+(2a)z+(2b)z=2(2ab+az+bz).xy+xz+yz=(2a)(2b)+(2a)z+(2b)z=2(2ab+az+bz).
Since 2ab+az+bz2ab+az+bz is an integer, xy+xz+yzxy+xz+yz is even.
Transcribed Image Text:3.46. Given below is a proof of a result. What is the result?
Proof Assume, without loss of generality, that x and y are even. Then x = 2a and y = 26 for integers a and
b. Therefore,
xy + xz+ yz = (2a) (26) + (2a) z+ (2b) z = 2 (2ab +az + bz) .
Since 2ab + az + bz is an integer, xy + xz+ yz is even.
Expert Solution
Step 1 : Given things are :-
Here we have given a proof of the results
We assume that x & y are even and z be any integer then we get xy+xz +yz as an even integer.
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