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Ac3

  • one year ago

Simplify the following expression. sqrt((1/(3(1+x)^(1/2))+(1/(3(1-x)^(1/2)))

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  1. freckles
    • one year ago
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    \[\sqrt{\frac{1}{3(1+x)^\frac{1}{2}}+\frac{1}{3(1-x)^\frac{1}{2}}}\] is this right?

  2. Ac3
    • one year ago
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    \[\sqrt{(\frac{ 1 }{ 3(1+x)^{1/2}})^{2}+(\frac{ 1 }{ 3(1-x)^{1/2} })^{2}}\]

  3. Ac3
    • one year ago
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    Forgot to square it

  4. Ac3
    • one year ago
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    This is the one.

  5. freckles
    • one year ago
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    \[\text{ by law of exponents you can write } (\frac{1}{3(1+x)^\frac{1}{2}})^2=\frac{1^2}{3^2(1+x)^\frac{2}{2}}...\] you can do the same with the other term inside that big square root thingy

  6. Ac3
    • one year ago
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    I know how to do it. I just want to see what someone else gets.

  7. Ac3
    • one year ago
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    I don't like my answer.

  8. freckles
    • one year ago
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    what did you get?

  9. Ac3
    • one year ago
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    \[\frac{ 1 }{ 3 }\sqrt{\frac{ 2 }{ 1-x^2 }}\]

  10. freckles
    • one year ago
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    that is what I have too.. \[\sqrt{\frac{1}{9(1+x)}+\frac{1}{9(1-x)}} \\ \sqrt{\frac{1}{9}} \sqrt{\frac{1}{1+x}+\frac{1}{1-x}} \\ \frac{1}{3} \sqrt{\frac{2}{1-x^2}} \]

  11. Ac3
    • one year ago
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    The reason I don't like it. Is because in these problems that I've been doing we tend to get rid of x in the expression through simplifying.

  12. freckles
    • one year ago
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    you can't get rid of x here though ...

  13. Ac3
    • one year ago
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    Since it's not disappearing makes me wonder that I did something wrong. However no matter how many times I go back I can't find anything wrong with my math.

  14. Ac3
    • one year ago
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    Take this last one for example.

  15. Ac3
    • one year ago
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    \[\sqrt{\frac{ (sinx)^2 }{ 2 }+(cosx)^2+\frac{ (sinx)^2 }{ 2 }}\]

  16. Ac3
    • one year ago
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    in that one we get rid of x. It all simplifies down to 1.

  17. freckles
    • one year ago
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    right because sin^2(x)+cos^2(x)=1 and the sqrt(1)=1

  18. Ac3
    • one year ago
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    exactly so that's why I'm a bit worried that we may be wrong. We usually tend to get rid of the x from inside of the radical at least.

  19. freckles
    • one year ago
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    if you want to rationalize the denominator you can but that would still leave x inside the radical in the numerator

  20. Ac3
    • one year ago
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    oh well, hopefully it's right. Thanks!

  21. freckles
    • one year ago
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    but the simplification you have is so far right if the problem really is: \[\sqrt{(\frac{1}{3(1+x)^\frac{1}{2}})^2+(\frac{1}{3(1-x)^\frac{1}{2}})^2}\]

  22. Ac3
    • one year ago
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    yes it is. It is right. On the next part of the problem it makes sense.

  23. Ac3
    • one year ago
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    Thanks!

  24. freckles
    • one year ago
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    np

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