Solving an equation with radicals

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SUMMARY

The discussion focuses on solving the equation √(x²/2 + 11) = x - 1, requiring answers in mixed radical form. The participant initially squared both sides, resulting in x²/2 + 11 = x² + 1, but incorrectly expanded the right side. The correct expansion of (x - 1)² is x² - 2x + 1, which is crucial for proceeding with the solution. The conversation emphasizes the importance of correctly applying the binomial expansion in algebraic manipulations.

PREREQUISITES
  • Understanding of radical equations
  • Familiarity with the quadratic formula
  • Knowledge of binomial expansion
  • Basic algebraic manipulation skills
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  • Practice solving radical equations with mixed radical forms
  • Review the quadratic formula and its applications
  • Study binomial expansion techniques in algebra
  • Explore common mistakes in algebraic manipulations
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Students studying algebra, particularly those tackling radical equations and preparing for exams in mathematics.

trulyfalse
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Hello and good evening! I'm having a fair bit of difficulty with this question, any help would be appreciated.

Homework Statement


√(x2/2+11)=x-1
Answers are required in mixed radical form.


Homework Equations


The quadratic formula/factoring will be useful near the end of the problem.


The Attempt at a Solution


I squared both sides of the equation to get
x2/2+11=x2+1
However I'm not quite sure how to proceed and whether eliminating the radical in the first step was the correct step.
 
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You are doing the right step but you squared the right side wrong. (x-1)^2 isn't equal to x^2+1. Try that again.
 
You're right! I completely forgot it was a binomial. Thanks for your help.
 

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