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Compgroupmail

  • 2 years ago

help solve 1/2X=-1+sqrt(x-2)

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  1. Compgroupmail
    • 2 years ago
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    correction \[\frac{ 1 }{ 2 }x=-1 +\sqrt{x+2}\]

  2. SheldonEinstein
    • 2 years ago
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    What you tried yet @Compgroupmail ?

  3. Compgroupmail
    • 2 years ago
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    I tried to bring it to the power by \[\frac{ 1 }{ 4 }x=1+(x+2)\] /is this correct?

  4. SheldonEinstein
    • 2 years ago
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    see (a+b)^2 is NOT equal to a^2 + b^2 only. \[\large{(\frac{1X}{2})^2 = (-1 + \sqrt{x-2})^2 }\] \[\large{\frac{x^2}{4} = 1 + x-2 - 2\sqrt{x-2} }\]

  5. SheldonEinstein
    • 2 years ago
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    Oh wait in your corrected question it is x+2 not x-2 so it will be : \[\large{\frac{x} = 1+x-2 -2\sqrt{x+2}}\]

  6. SheldonEinstein
    • 2 years ago
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    \[\large{\frac{x^2}{4} = 1+x-2 -2\sqrt{x+2}}\]

  7. Compgroupmail
    • 2 years ago
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    ok but I still don't understand how you broke it down to that. Can we go through it step by step?

  8. SheldonEinstein
    • 2 years ago
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    Oh! Sorry I think I confused you, yes why not... so do you know the identity of (a+b)^2 = ?

  9. Compgroupmail
    • 2 years ago
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    a^2+2ab+b^2

  10. SheldonEinstein
    • 2 years ago
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    Right! so in RHS (Right hand side) we have : -1 + sqrt{x+2} , correct?

  11. Compgroupmail
    • 2 years ago
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    left side of equation \[(\frac{ 1 }{ 2 }x)^2= \frac{ 1 }{ 4 }x\]. Correct?

  12. Compgroupmail
    • 2 years ago
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    right. That is the right hand side. What's next?

  13. SheldonEinstein
    • 2 years ago
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    Yes , so square the right hand side ... that is : \[\large{( \sqrt{x+2} - 1 )^2 }\] Can you square that?

  14. Compgroupmail
    • 2 years ago
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    no. Not 100% how to do it. That's what's messing me up.

  15. SheldonEinstein
    • 2 years ago
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    Wait for 1 minute, I am opening google chrome as IE is quite slow

  16. Compgroupmail
    • 2 years ago
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    ok no problem

  17. Algebraic!
    • 2 years ago
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    add 1 to both sides and square both sides \[(\frac{ x }{ 2 } +1)^2 = x +2\]

  18. Algebraic!
    • 2 years ago
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    \[ \frac{ x^2 }{4 } +x +1 = x+2\]

  19. Algebraic!
    • 2 years ago
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    x^2 =4

  20. Compgroupmail
    • 2 years ago
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    ahh. I understand now :) THanks!

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