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anonymous

  • 5 years ago

square root of 2z+9-square root of z+6=o

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  1. anonymous
    • 5 years ago
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    \[\sqrt{2z+9 }-\sqrt{z+6}=0\]

  2. anonymous
    • 5 years ago
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    \[\sqrt{2z+9}=\sqrt{z+6}\]

  3. anonymous
    • 5 years ago
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    \[\implies \sqrt{2z+9}=\sqrt{z+6} \implies 2z+9=z+6 \implies z=-3\] Plug in the equation and check!!

  4. anonymous
    • 5 years ago
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    hows the work?

  5. anonymous
    • 5 years ago
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    Just substitute in the original equation with z=-3 to check it's the right solution!!

  6. anonymous
    • 5 years ago
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    It's right by the way!! So your answer is z=-3

  7. anonymous
    • 5 years ago
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    yea i checked!

  8. anonymous
    • 5 years ago
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    \[\sqrt{x+8}=x-4\]

  9. anonymous
    • 5 years ago
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    What do you think?

  10. anonymous
    • 5 years ago
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    x-8=x-16

  11. anonymous
    • 5 years ago
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    -8 -8

  12. anonymous
    • 5 years ago
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    =8

  13. anonymous
    • 5 years ago
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    Well. The first thing you should here is to get rid of the square root. To do so, you should square both sides. Can you do that?

  14. anonymous
    • 5 years ago
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    yess

  15. anonymous
    • 5 years ago
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    you should do*

  16. anonymous
    • 5 years ago
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    Ok. Do it and show me what you get.

  17. anonymous
    • 5 years ago
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    \[\sqrt({x-8})^{2}=(x-4)^{2}\]

  18. anonymous
    • 5 years ago
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    \[x+8=x+16\]

  19. anonymous
    • 5 years ago
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    are you sure about the right hand side?

  20. anonymous
    • 5 years ago
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    (x-4)^2 is what?

  21. anonymous
    • 5 years ago
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    yes because 4x4=16

  22. anonymous
    • 5 years ago
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    all (x-4) is raised to the power of 2. Not only the 4.. So it's like (x-4) times (x-4)

  23. anonymous
    • 5 years ago
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    ??

  24. anonymous
    • 5 years ago
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    :)

  25. anonymous
    • 5 years ago
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    Ok.. follow my steps carefully!

  26. anonymous
    • 5 years ago
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    First start by squaring both sides: \[(\sqrt{x+8})^2=(x-4)^2\] you did the left hand side, it's the same as x+8.. the right hand side is: \[(x-4)^2=x^2-8x+16\]

  27. anonymous
    • 5 years ago
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    Now, the equation will look like: \[x+8=x^2-8x+16 \implies x^2-9x+8=0\] Do you know how to solve a quadratic equation?

  28. anonymous
    • 5 years ago
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    Just factorize the expression x^2-9x+8 to get: \[x^2-9x+8=0 \implies (x-8)(x-1)=0 \implies x=1, x=8\] We have two values for x. Check for each one!

  29. anonymous
    • 5 years ago
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    You will find that only x=8 is a solution of the equation.

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