My Math Forum  

Go Back   My Math Forum > Math Forums > Math Software

Math Software Math Software - Mathematica, Matlab, Calculators, Graphing Software


Thanks Tree8Thanks
Reply
 
LinkBack Thread Tools Display Modes
September 18th, 2018, 01:54 PM   #1
Newbie
 
Joined: Sep 2018
From: tunis

Posts: 27
Thanks: 0

how to show that 2n + 1 = x ^ 2 ?

how to show that 2n + 1 = x ^ 2 ?
the solution is:
n = 2 * (m ^ 2 - m)
x = 1 - 2 * m
and
1 + 3b + 3b ^ 2 = x ^ 3
the solution is:
b = -1, x = 1
step by step
I calculated that with a software it gives only the solution.
Thank you.

Last edited by skipjack; September 19th, 2018 at 10:27 AM.
Ak23 is offline  
 
September 18th, 2018, 02:54 PM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 19,700
Thanks: 1804

For the second problem, the software didn't find the solution b = 0, x = 1.

Last edited by skipjack; September 19th, 2018 at 10:27 AM.
skipjack is online now  
September 18th, 2018, 07:24 PM   #3
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 1,888
Thanks: 767

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by Ak23 View Post
how to show that 2n + 1 = x ^ 2 ?
the solution is:
n = 2 * (2 ^ m-m)
x = 1-2 * m
and
1 + 3b + 3b ^ 2 = x ^ 3
the solution is:
b = -1, x = 1
step by step
I calculated that with a software it gives only the solution.
thank you.
I think we can simplify this a bit and get rid of the "x", computer or not. If we have $\displaystyle n^2$ then we can get the next square (integer) by adding 2n + 1. ie. $\displaystyle (n + 1)^2 = (n^2) + (2n + 1)$

Similar for the cube:
$\displaystyle (n + 1)^3 = (n^3) + (3n^2 + 3n + 1)$

-Dan
Thanks from Ak23
topsquark is offline  
September 19th, 2018, 12:15 AM   #4
Newbie
 
Joined: Sep 2018
From: tunis

Posts: 27
Thanks: 0

@topsquark
2n+1=4n+2
2n-4n=-1
2n=-1
n=-1/2

2.(-1/2)+1 =0
it does not work
pair = odd

Last edited by Ak23; September 19th, 2018 at 12:17 AM.
Ak23 is offline  
September 19th, 2018, 03:28 AM   #5
Newbie
 
Joined: Sep 2018
From: tunis

Posts: 27
Thanks: 0

n=2*(m^2-m)
x=1-2*m
is solution
when
z^2=(n+1)^2
y^2=n^2
x^2=2n+1
It's not all numbers
only with the squares that is on the odd numbers
1 3 5 7 9 11, .... 2N-1
9 25 49 .... ETC
Ak23 is offline  
September 19th, 2018, 03:56 AM   #6
Newbie
 
Joined: Sep 2018
From: tunis

Posts: 27
Thanks: 0

m n x x^2
0 0 1 1
1 0 -1 1
2 4 -3 9
3 12 -5 25
4 24 -7 49

Last edited by Ak23; September 19th, 2018 at 03:59 AM.
Ak23 is offline  
September 19th, 2018, 05:17 AM   #7
Global Moderator
 
Joined: Dec 2006

Posts: 19,700
Thanks: 1804

If x is odd, it can be written as 1 - 2m.

That means that x² = 4m² - 4m + 1 = 2(2m² - 2m) + 1 = 2n + 1, where n = 2(m² - m).

If you have no objection, I'll correct your error in the original post, so that the thread can be shortened.
Thanks from Ak23
skipjack is online now  
September 19th, 2018, 05:59 AM   #8
Newbie
 
Joined: Sep 2018
From: tunis

Posts: 27
Thanks: 0

how to find solutions?
for x ^ 2 and x ^ 3
Ak23 is offline  
September 19th, 2018, 06:34 AM   #9
Global Moderator
 
Joined: Dec 2006

Posts: 19,700
Thanks: 1804

Doesn't my previous post show how to find the solutions for x²?
Thanks from Ak23
skipjack is online now  
September 19th, 2018, 07:33 AM   #10
Newbie
 
Joined: Sep 2018
From: tunis

Posts: 27
Thanks: 0

yes I understood thank you very much
Ak23 is offline  
Reply

  My Math Forum > Math Forums > Math Software

Tags
show



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
show mared Geometry 7 May 16th, 2015 09:50 PM
Show that ... Few_But_Ripe Complex Analysis 1 November 11th, 2011 09:08 AM
want to show that show that two infinite summations R equal notnaeem Real Analysis 4 August 16th, 2010 12:32 PM
show that : naserellid Algebra 2 August 15th, 2010 02:20 AM





Copyright © 2018 My Math Forum. All rights reserved.