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pratu043

  • 3 years ago

Find x.

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  1. pratu043
    • 3 years ago
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    |dw:1342256143778:dw|

  2. waterineyes
    • 3 years ago
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    Try by rationalization process...

  3. georgeblue22
    • 3 years ago
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    |dw:1342256275514:dw|

  4. waterineyes
    • 3 years ago
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    Multiply and divide both the sides by: \[\sqrt{x+4}-\sqrt{x -3}\]

  5. pratu043
    • 3 years ago
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    You mean multiply by \[(\sqrt{x+4} - \sqrt{x-3})/(\sqrt{x+4} - \sqrt{x-3})\]

  6. waterineyes
    • 3 years ago
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    Yes...

  7. ganeshie8
    • 3 years ago
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    check @georgeblue22 once.. its very simple

  8. pratu043
    • 3 years ago
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    |dw:1342256415787:dw|

  9. ganeshie8
    • 3 years ago
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    i mean check @georgeblue22 reply once

  10. waterineyes
    • 3 years ago
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    No no don't do this...

  11. pratu043
    • 3 years ago
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    I don't understand @georgeblue22's reply.

  12. waterineyes
    • 3 years ago
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    just do what @georgeblue22 said.. I was thinking it as an expression but it is an equation.. I forgot to see there 1 on right hand side...

  13. TheViper
    • 3 years ago
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    \[\Huge{\color{gold}{\star \star}{\color{orange}{\text{Rationlise}}}}\]

  14. TheViper
    • 3 years ago
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    best hint

  15. pratu043
    • 3 years ago
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    Oh yes, he brought the denominator to the other side.

  16. TheViper
    • 3 years ago
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    yes @pratu043

  17. waterineyes
    • 3 years ago
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    See, multiply both the sides by : \(\sqrt{x+4}+\sqrt{x -3}\)..

  18. pratu043
    • 3 years ago
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    That will help to get of the square root on the left side.

  19. TheViper
    • 3 years ago
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    Understood @pratu043 ??? :)

  20. waterineyes
    • 3 years ago
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    You will left with only one square root term.... after solving..

  21. pratu043
    • 3 years ago
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    Left side will be: |dw:1342256668499:dw|

  22. waterineyes
    • 3 years ago
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    No you are doing wrong..

  23. pratu043
    • 3 years ago
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    What's the mistake?

  24. georgeblue22
    • 3 years ago
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    |dw:1342256752422:dw|

  25. Aditi_Singh
    • 3 years ago
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    Did you try squaring on both the sides ?

  26. waterineyes
    • 3 years ago
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    See show me what you get after multiply the term I said above... Do it slowly...

  27. pratu043
    • 3 years ago
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    Which term?

  28. pratu043
    • 3 years ago
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    So 7 = sqrt(x + 4) + sqrt(x - 3).

  29. waterineyes
    • 3 years ago
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    \[\frac{(\sqrt{x+4} - \sqrt{x-3})}{(\sqrt{x+4} + \sqrt{x-3})} \times (\sqrt{x+4} + \sqrt{x-3}) = 1 \times (\sqrt{x+4} + \sqrt{x-3})\] Now solve this..

  30. waterineyes
    • 3 years ago
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    You will be left with: \[\sqrt{x+4}- \sqrt{x-3} = \sqrt{x+4} + \sqrt{x-3}\] Now look it properly what is the term that is getting cancelling on both the sides???

  31. pratu043
    • 3 years ago
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    sqrt(x + 4).

  32. waterineyes
    • 3 years ago
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    Yes then cancel it and tell me what you are left with now..

  33. pratu043
    • 3 years ago
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    |dw:1342257083455:dw|

  34. waterineyes
    • 3 years ago
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    Can you bring them on one side now??

  35. pratu043
    • 3 years ago
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    |dw:1342257134878:dw|

  36. waterineyes
    • 3 years ago
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    Yes add them...

  37. pratu043
    • 3 years ago
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    |dw:1342257180914:dw|

  38. waterineyes
    • 3 years ago
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    Yes... Have faith you are in a right direction.. Now squaring both the sides what will you get??

  39. TheViper
    • 3 years ago
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    sqaure both sides @pratu043

  40. pratu043
    • 3 years ago
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    |dw:1342257244043:dw|

  41. waterineyes
    • 3 years ago
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    And then put the brackets = 0 and find x from here..

  42. pratu043
    • 3 years ago
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    |dw:1342257276476:dw|

  43. waterineyes
    • 3 years ago
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    Yes.. You are right...

  44. TheViper
    • 3 years ago
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    yes @pratu043 u got it ;) deserve a medal ;)

  45. pratu043
    • 3 years ago
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    Thanks!!!

  46. TheViper
    • 3 years ago
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    yw ;)

  47. waterineyes
    • 3 years ago
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    See @pratu043 if we are given with: \[\large (x-1)(y-2) = 0\] then you can do directly this: \[(x - 1) =0 \quad and \quad (y - 2) = 0\] Getting???

  48. waterineyes
    • 3 years ago
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    So at the end we are left with: \[4(x-3) = 0\] As \(4 \ne 0\) So, You can put directly: \[(x-3) = 0\] \[x = 3\]

  49. pratu043
    • 3 years ago
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    Oh I see .... I never knew that.

  50. waterineyes
    • 3 years ago
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    But this is possible in case we have 0 in right hand side.. Be careful...

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