Solving an equation with radicals

  • Thread starter trulyfalse
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In summary, the conversation involved a student seeking help with a math problem involving a mixed radical form. The suggested approach was to use the quadratic formula or factoring. The student attempted to solve the problem by squaring both sides of the equation, but was reminded to correctly square the binomial on the right side. The student expressed gratitude for the help provided.
  • #1
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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  • #2
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.
 
  • #3
You're right! I completely forgot it was a binomial. Thanks for your help.
 

1. What is a radical?

A radical is a mathematical symbol (√) used to represent the square root of a number. It can also be used to represent higher roots, such as cube roots (∛) or fourth roots (∜).

2. How do I solve an equation with radicals?

To solve an equation with radicals, you need to isolate the radical term on one side of the equation and then square both sides to eliminate the radical. Repeat this process until all radicals are eliminated, and then solve for the variable using basic algebraic principles.

3. Can I have a radical on both sides of the equation?

Yes, you can have a radical on both sides of the equation. However, it may make the equation more difficult to solve, so it is often helpful to eliminate one of the radicals by squaring both sides before continuing with the solution process.

4. What if the radical is inside parentheses?

If the radical is inside parentheses, you can use the exponent rule for radicals to rewrite it as a fractional exponent. Then, you can distribute the exponent to the terms inside the parentheses and continue solving the equation as usual.

5. Are there any special cases when solving equations with radicals?

Yes, there are a few special cases that may arise when solving equations with radicals. These include extraneous solutions, where the solution may not be valid for the original equation, and imaginary solutions, where the solution involves the imaginary number i (√-1). It is important to check for these cases and discard any invalid solutions.

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