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JozelynW

  • one year ago

Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model.

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  1. JozelynW
    • one year ago
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    How to make a extraneous solution?

  2. JozelynW
    • one year ago
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    @ikram002p

  3. JozelynW
    • one year ago
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    @welshfella

  4. JozelynW
    • one year ago
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    do you know how to write a extraneous radical equation

  5. xapproachesinfinity
    • one year ago
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    extraneous sol is solution that is not in the domain of the equation you started with

  6. JozelynW
    • one year ago
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    huh

  7. JozelynW
    • one year ago
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    well, then how do I create a radical extraneous equation?

  8. xapproachesinfinity
    • one year ago
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    consider the following equation \(\sqrt{\frac{x+1}{x}}=\sqrt{\frac{1}{x}}\) see that x=0 is not in the domain try to solve that equation

  9. xapproachesinfinity
    • one year ago
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    it is easier to create an equation with correct solution (not extraneous )

  10. welshfella
    • one year ago
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    -3 sqrt(7 + 2x) = 24 sqrt(7 + 2x) = -8 square both sides 7 + 2x = 64 2x = 57 x = 57/2 now plug in x = 57/2 and see if it satisfies the original equation

  11. xapproachesinfinity
    • one year ago
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    consider the following equation \(\sqrt{x+1}=\sqrt{3x-1}\) solution is \(x=1\) if we check it on the equation we it checks out

  12. JozelynW
    • one year ago
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    it wants me to use this equation a√x+b+c=d

  13. xapproachesinfinity
    • one year ago
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    you just said radical equation you did specify any details

  14. xapproachesinfinity
    • one year ago
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    well at any rate check @welshfella work

  15. JozelynW
    • one year ago
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    I know because then you would just be giving me answers and then people would be thinking that im cheating

  16. welshfella
    • one year ago
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    a negative number times a radical will give an extraneous solution

  17. JozelynW
    • one year ago
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    so i just wanted to know how to create a radical extraneous equation

  18. JozelynW
    • one year ago
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    can you give me an example

  19. welshfella
    • one year ago
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    if you plug in 57/2 into the above it won't give you 24

  20. JozelynW
    • one year ago
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    but it's suppose to

  21. JozelynW
    • one year ago
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    28.5

  22. welshfella
    • one year ago
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    no - ones like that will give an extraneous solution When you square you get a positive result so a negative value can get 'lost'.

  23. JozelynW
    • one year ago
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    so 28.5 is not 57/2

  24. welshfella
    • one year ago
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    -3 * sqrt(7 + 28.5) = -17.87

  25. JozelynW
    • one year ago
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    what do you mean sqrt ? sqrt of 3

  26. welshfella
    • one year ago
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    do you see that this is an extraneous solution?

  27. welshfella
    • one year ago
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    square root of (7 + 28.5)

  28. JozelynW
    • one year ago
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    i do it equals -17.87

  29. JozelynW
    • one year ago
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    wait did something wrong

  30. JozelynW
    • one year ago
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    sqrt of 35.5 =5.95 and 5.95 times -3 equals -17.87

  31. welshfella
    • one year ago
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    yes that is correct so 28.5 is not a solution its extraneous

  32. welshfella
    • one year ago
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    now one that does not have an extraneous solution would be sqrt(4x + 1) = 7 so 4x + 1 = 49 4x = 48 x = 12 which will fit the original equation

  33. welshfella
    • one year ago
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    here is a link which deals with the subject http://www.purplemath.com/modules/solverad2.htm

  34. JozelynW
    • one year ago
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    what are the options

  35. welshfella
    • one year ago
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    what do you mean?

  36. JozelynW
    • one year ago
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    you said " which will fit the original equation"

  37. welshfella
    • one year ago
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    I meant if you replace x by 12 in the original equation then the equation will balance the left side will equal 7

  38. welshfella
    • one year ago
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    sqrt(4*12 + 1) = sqrt 49 = 7

  39. welshfella
    • one year ago
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    so x = 12 is a valid solution

  40. JozelynW
    • one year ago
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    so the rule to this is.......

  41. welshfella
    • one year ago
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    a negative value as above will give an extraneous solution. But there' more to it than that that's why i posted the link. Some equations will have one valid and one extraneous solution , for example.

  42. welshfella
    • one year ago
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    sorry but i have to go now

  43. JozelynW
    • one year ago
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    thank you so much for you help @welshfella

  44. welshfella
    • one year ago
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    yw

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