My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree4Thanks
  • 3 Post By Olinguito
  • 1 Post By the john
Reply
 
LinkBack Thread Tools Display Modes
April 6th, 2014, 12:47 PM   #1
Senior Member
 
Joined: Nov 2013

Posts: 434
Thanks: 8

find

x^3 +4x =8
find
x^7+ 64x^2
mared is offline  
 
April 6th, 2014, 02:28 PM   #2
Senior Member
 
Olinguito's Avatar
 
Joined: Apr 2014
From: Greater London, England, UK

Posts: 320
Thanks: 155

Math Focus: Abstract algebra
$\displaystyle \begin{array}{rcl}x^3+4x &=& 8 \\\\

x^3 &=& 8-4x \\\\

x^6 &=& 64-64x+16x^2 \\\\

x^6+64x &=& 16x^2+64\ =\ 16(x^2+4) \\\\

x^7+64x^2 &=& 16(x^3+4x)\ =\ 16\cdot8\ =\ 128\end{array}$
Thanks from soroban, MarkFL and Denis

Last edited by Olinguito; April 6th, 2014 at 02:34 PM.
Olinguito is offline  
April 6th, 2014, 05:49 PM   #3
Senior Member
 
Joined: Mar 2014

Posts: 112
Thanks: 8

We need to know that we need to multiply both sides of the equation by $\displaystyle x^4$ to arrive at $\displaystyle x^7\,+\,64x^2$ for the expression $\displaystyle x^7$ so $\displaystyle x^7\,+\,4x^5\,=\,8x^4\text{.}$
We also need to know that we need to multiply both sides of the equation by $\displaystyle 16x$ to arrive at $\displaystyle x^7\,+\,64x^2$ for the expression $\displaystyle 64x^2$ so $\displaystyle 16x^4\,+\,64x^2\,=\,128x\text{.}$
Since $\displaystyle x^7\,=\,8x^4\,-\,4x^5$ and $\displaystyle 64x^2\,=\,128x\,-\,16x^4$ we get $\displaystyle x^7\,+\,64x^2\,=\,-4x^5\,-\,8x^4\,+\,128x\,=\,-4x^5\,-\,16x^3\,+\,16x^3\,-\,8x^4\,-\,32x^2\,+\,32x^2\,+\,128x\,=\,-4x^2(x^3\,+\,4x)\,-\,8x(x^3\,+\,4x)\,+\,16x^3\,+\,32x^2\,+\,128x\,=\,-32x^2\,-\,64x\,+\,16x^3\,+\,32x^2\,+\,128x\,=\,16x^3\,+\,6 4x\,=\,16(x^3\,+\,4x)\,=\,16\,\times\,8\,=\,\boxed {128}\text{.}$
Thanks from Olinguito
the john is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
find



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find Sk and Find Kv ( i got example formula below) kingkos Algebra 5 November 24th, 2012 11:40 PM
I want to find the distance in algebra find it kevinman Algebra 8 March 8th, 2012 05:53 AM





Copyright © 2018 My Math Forum. All rights reserved.