Solve equation with square roots

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SUMMARY

This discussion focuses on solving the equation involving square roots, specifically the expression $$x^2(x+3)=4$$. Participants emphasize the importance of simplifying expressions and removing fractions to find possible solutions for x. The correct solutions identified are $$x=2$$ and $$x=-2$$, with a cautionary note that not all identified roots are valid. The discussion highlights the necessity of verifying potential solutions to ensure accuracy.

PREREQUISITES
  • Understanding of algebraic expressions and equations
  • Familiarity with square root operations
  • Knowledge of simplifying fractions in mathematical expressions
  • Ability to verify solutions in polynomial equations
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  • Study methods for simplifying algebraic expressions
  • Learn techniques for solving polynomial equations
  • Explore the process of verifying roots in equations
  • Investigate the implications of extraneous solutions in algebra
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Students learning algebra, educators teaching mathematical problem-solving, and anyone interested in mastering the techniques for solving equations involving square roots and polynomials.

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Can someone show me step by step guide,how to find all possible solutions for example?
 

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andreask said:
Can someone show me step by step guide,how to find all possible solutions for example?
Hi Andreas, and welcome to MHB. You do not say what you have tried in order to tackle this problem. I suggest that you start by looking at those square roots. Can you simplify them at all?
 
Thanks for welcome! I need to remove fractions,and get possible solutions for X. I don't know how to remove fractions,step by step would be very useful.
 
Is the solution x^3+3x^2=4?
 
Hello,
nfmja0.jpg


Regards,
$$|\pi\rangle$$
 
Thanks Petrus, can you continue?
 
Or someone else? Its urgent. Thanks.
 
Hello,
I Will post how to solve it after you post what you think you should do! Tips Dont do the homework in the last minutes

Regards,
$$|\pi\rangle$$
 
Expression skould be without fractions,and then i have to find possible solution(s) for X.
 
  • #10
andreask said:
Is the solution x^3+3x^2=4?
Hello,
My bad did not see this but that is correct! So what is x equal to?

Regards,
$$|\pi\rangle$$
 
  • #11
I think it can be only one! True?
 
  • #12
I want to know how do i get solution in math way. I can see that is 1,but how do i prove it? Can i "disassemble" my last expression? Or if you have time,show me please how would you do it! And many thanks,and sorry for my English!
 
  • #13
Hello,
$$x^2(x+3)=4$$ and you suspect that $$x=1,2,-2$$ BUT you always check if they are correct and Then you see that $$x=2,-2$$ is a fake root!

Regards,
$$|\pi\rangle$$
 
Last edited:

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