KatKingston9031 KatKingston9031
  • 02-10-2019
  • Mathematics
contestada

Prove that for all positive integers x and x3 have the same odd/even status. (Hint: proof by cases)

Respuesta :

lyndalau86
lyndalau86 lyndalau86
  • 04-10-2019

Answer:

See explanation below

Step-by-step explanation:

Case 1) x is even ⇒ x³ is even

x = 2k for some k

⇒x³ = (2k)³= 8k³ = 2(4k³) which is even.

Case 2) x is odd⇒x³ is odd

x = 2k - 1 for some k

⇒x³ = (2k - 1)³ = (2k)³- 3(2k)²(1) + 3(2k)(1)² -(1)³ = 8k³- 12k² + 6 - 1 = 2 (4k³ - 6k² + 3) - 1 which is odd.

Answer Link

Otras preguntas

Shays' Rebellion encouraged national leaders to A. seek alternatives to the Articles of Confederation. B. repeal the Stamp Act. C. change the Declaration of In
Polls are taken to a. guarantee the constitutional rights of all people. b. determine people's attitudes and viewpoints. c. further the political socialization
The first pesticides relied on natural chemicals, such as those taken from chrysanthemum flowers. a. True b. False
1468:22-6+8888-998=????????
A quantity that has magnitude only is a _____. scalar diagonal vector
Change the fraction 93/1,000 to a decimal. A. 0.00093 B. 0.93 C. 0.0093 D. 0.093
If a carbon atom is bonded to two hydrogen atoms and two carbon atoms, what type of bond must exist between the carbon atoms?
What is the definition of tropical storm?
What value of k makes the statement true? –(k + 12) = 6 + (–12) A. –18 B. –6 C. 6 D. 18
What is negative 8 minus negative 4?