Is This Equation Solvable: 2*x^2*(x-2)^2 = x+1?

  • Context: High School 
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Discussion Overview

The discussion revolves around the solvability of the equation 2*x^2*(x-2)^2 = x+1. Participants explore methods for simplifying and solving the equation, including algebraic manipulations and potential roots.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant suggests using algebraic manipulations to simplify the equation, such as multiplying out brackets and collecting like terms.
  • Another participant notes that the equation can be transformed into a third-order polynomial and mentions that there are formulas available for solving such equations analytically.
  • Some participants highlight the possibility of finding a simple root by inspection or graphical methods, which could facilitate further factoring and solving.
  • There is a correction regarding the interpretation of the equation, with one participant initially misreading a symbol, which they later acknowledge.

Areas of Agreement / Disagreement

Participants generally agree on the approach of simplifying the equation and the existence of a simple root, but there is no consensus on the specific methods or solutions to be applied.

Contextual Notes

Limitations include the potential for misinterpretation of the equation and the need for further clarification on the algebraic steps involved in solving the third-order polynomial.

haiha
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My friend asks me to solve this one, but i have no idea :

2*x^2*(x-2)^2 = x+1.

Thanks for any hints.
 
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When you have a complicated-looking equation, you should use whatever knowledge you have of algebraic manipulations, to simplify it.

Multiply out brackets... collect like terms... eventually you'll be able to put it into a form that you recognise.

Also I think your question should go in the homework forums.

ETA: huh, I thought that '*' in the middle of the LHS was a '+'. Your version looks harder! Never mind, try simplifying anyway.
 
Last edited:
You advice still stands - multiply out and factor. Notice that there is a root you can spot from the original form by inspection.
 
If you wrote the equation without mistake: 2*x^2*(x-2)^2 = x+1 ,
then a few simple calculations will lead you to a third order equation, and there are formulas for solving analtically a third order polynimial equation.

However, as matt_grime said, there is one root that is easy to find: just try a few numbers, or make a graphic of the function to guess what is this simple root.

Once you have found this simple root, you can indeed factor it out by division and solve the second order polynomial that still remains.
 
Thanks for all the helps. I will try it. Anyway, it is not a homework for sure.
 

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