Prove the following statements: i. Let x, y and z be integers. If exactly one of x,y and z is odd then xy + yz isS even. ii. If x and y are real numbers then x2 > 4y(x – y). -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 40E
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3. Q3; Proof Methods
Prove the following statements:
i. Let x, y and z be integers. If exactly one of x, y and z is odd then
Xy + yz is even.
ii. If x and y are real numbers then x2 > 4y(x – y).
iii. Suppose that a, b, c and d are positive integers, prove that a+2c+
d or b – a + 2d if and only if b+ 2c + 3d or 3a + 4c + b.
|
Transcribed Image Text:3. Q3; Proof Methods Prove the following statements: i. Let x, y and z be integers. If exactly one of x, y and z is odd then Xy + yz is even. ii. If x and y are real numbers then x2 > 4y(x – y). iii. Suppose that a, b, c and d are positive integers, prove that a+2c+ d or b – a + 2d if and only if b+ 2c + 3d or 3a + 4c + b. |
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