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P->Q

  • 2 years ago

1/x^2 + 1/x =6 solve for x

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  1. petewe
    • 2 years ago
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    make the left side into 1 equation.

  2. asnaseer
    • 2 years ago
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    multiply both sides by\(x^2\) and solve the resulting quadratic equation.

  3. P->Q
    • 2 years ago
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    \[x^2/ x^2 + x^2/x^2 = 6x^2\]

  4. P->Q
    • 2 years ago
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    2x^2 = 6x^2

  5. asnaseer
    • 2 years ago
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    the denominator of your second term above is wrong

  6. asnaseer
    • 2 years ago
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    you should get:\[x^2/ x^2 + x^2/x = 6x^2\]

  7. asnaseer
    • 2 years ago
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    next - simplify each term

  8. P->Q
    • 2 years ago
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    but dont they need to have the same denominator to add

  9. asnaseer
    • 2 years ago
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    what does \(x^2/x^2\) equal?

  10. P->Q
    • 2 years ago
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    1

  11. asnaseer
    • 2 years ago
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    correct - now simplify the next term

  12. P->Q
    • 2 years ago
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    1+ x= 6x^2

  13. asnaseer
    • 2 years ago
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    thats right - now re-arrange this into a standard form, i.e into the form \(ax^2+bx+c=0\) and then solve

  14. P->Q
    • 2 years ago
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    so I did quadratic equation and go -1 plus or minus radical 25 all over -12

  15. asnaseer
    • 2 years ago
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    doesn't look right - can you please show your steps so that I can help spot where you may have made a mistake?

  16. P->Q
    • 2 years ago
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    k, u said put it into the standard form so I started from 1 + x = 6x^2 -6x^2 + x+1 = 0 a= -6, b= 1, c= 1 \[-1\pm \sqrt{1^{2}-4(-6)(1) \over 2(-6)}\]

  17. P->Q
    • 2 years ago
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    then got -1 plus or minus radical 25 all over -12

  18. asnaseer
    • 2 years ago
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    oh - sorry - I misread

  19. asnaseer
    • 2 years ago
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    you are right - and you know what \(\sqrt{25}\) equals?

  20. asnaseer
    • 2 years ago
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    the formula you used doesn't look quite right, it should be:\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

  21. asnaseer
    • 2 years ago
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    the WHOLE thing should be divided by 2a

  22. asnaseer
    • 2 years ago
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    so you should have got:\[\frac{-1\pm \sqrt{1^{2}-4(-6)(1)}}{2(-6)}\]

  23. P->Q
    • 2 years ago
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    o ok so um x = 1/-3 and x = 1/2

  24. asnaseer
    • 2 years ago
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    perfect!

  25. P->Q
    • 2 years ago
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    ya I ment to put all over 2a but I was trying to make it come out nice and pretty in the equation thing but it took lng

  26. asnaseer
    • 2 years ago
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    although you should write it as: x=-1/3 or 1/2

  27. asnaseer
    • 2 years ago
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    you don't usually put the minus sign in the denominator

  28. P->Q
    • 2 years ago
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    wow these are so frustrating I was literally about to give up and go home, im in a library trying to study and there are all these other students basically hanging out and talking and there are no available tutors

  29. asnaseer
    • 2 years ago
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    also note that you should use the word "or" rather than "and" here. i.e. x = -1/3 or 1/2 instead of x = -1/3 and 1/2 because x canot equal both values at the same time

  30. P->Q
    • 2 years ago
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    ok ill do that

  31. P->Q
    • 2 years ago
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    thanks a lot you gave me a little hope to keep pushing a little more

  32. asnaseer
    • 2 years ago
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    great - and keep persevering - you'll get the hang of these very soon I'm sure :)

  33. asnaseer
    • 2 years ago
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    yw :)

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