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anonymous

  • 5 years ago

Hi I need to find the solution set for the following equation √(10x+5) - √(6x-11) =6

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  1. anonymous
    • 5 years ago
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    you sure that is a "-" and not a "+"?

  2. anonymous
    • 5 years ago
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    Yes the equation is correct

  3. anonymous
    • 5 years ago
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    too bad because if it was a +, 2 would work by inspection. this problem is a pain. you have to square twice

  4. anonymous
    • 5 years ago
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    And it says solve the equation. The solution set is blank and blank

  5. anonymous
    • 5 years ago
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    ok let me work it out. i was trying to guess what would give a perfect square for 10x+5 and 6x-11

  6. anonymous
    • 5 years ago
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    Thx

  7. anonymous
    • 5 years ago
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    2 works because 2*10+5=25 and 6*2-11=1

  8. anonymous
    • 5 years ago
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    and 5+1=6

  9. anonymous
    • 5 years ago
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    So would the sol set be 5,1

  10. anonymous
    • 5 years ago
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    no the solution would be x = 2, but it is not. i am still working.

  11. anonymous
    • 5 years ago
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    have to square both sides, then square again. i will show you but i want to get a correct answer so i don't blow it.

  12. anonymous
    • 5 years ago
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    good heavens. i will be back in ten minutes with the answer and the algebra. hold on.

  13. anonymous
    • 5 years ago
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    K :-)

  14. anonymous
    • 5 years ago
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    62

  15. anonymous
    • 5 years ago
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    is the answer

  16. anonymous
    • 5 years ago
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    would you like a worked out solution?

  17. anonymous
    • 5 years ago
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    square both sided. you will get \[16x-6-2\sqrt{(10x+5)(6x-11)}=36\]

  18. anonymous
    • 5 years ago
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    \[-2\sqrt{(10x+5)(6x-11)}=42-16x\]

  19. anonymous
    • 5 years ago
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    divide by -2 \[\sqrt{(10x+5)(6x-11)}=8x-21\]

  20. anonymous
    • 5 years ago
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    so is there only one solution of 62

  21. anonymous
    • 5 years ago
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    sorry my computer is slow

  22. anonymous
    • 5 years ago
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    then square again. you will get \[(10x-5)(6x-11)=(8x+21)^2\]

  23. anonymous
    • 5 years ago
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    yes only one answer. you will solve a quadratic and get two solutions but only one will work.

  24. anonymous
    • 5 years ago
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    introduced a false solution when you squared

  25. anonymous
    • 5 years ago
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    typo on last answer. it should have been \[(10x+5)(6x-11)=(8x-21)^2\]

  26. anonymous
    • 5 years ago
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    thx u

  27. anonymous
    • 5 years ago
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    expand these to get \[60x^2-80x-55=64x^2-336x+441\]

  28. anonymous
    • 5 years ago
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    set =0 and solve: \[4x^2-256x+496=0\] divide by 4 \[x^2-64x+124=0\]

  29. anonymous
    • 5 years ago
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    factor \[(x-62)(x-2)=0\] \[x=62\] or \[x=2\]

  30. anonymous
    • 5 years ago
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    but there is only one answer because 2 does not work. if you replace x by 2 in the original equation you get \[\sqrt{25}-\sqrt{1}=6\] \[5-1=6\] which is false.

  31. anonymous
    • 5 years ago
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    negatives on both?? thx

  32. anonymous
    • 5 years ago
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    62 will work but only 62, not 2.

  33. anonymous
    • 5 years ago
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    oh negatives on both when factoring. but the only answer is x = 62

  34. anonymous
    • 5 years ago
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    you have to plug it into the original equation

  35. anonymous
    • 5 years ago
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    \[\sqrt{10\times 62+5}-\sqrt{6\times 62-11}\] \[\sqrt{625}-\sqrt{361}=25-19=6\]

  36. anonymous
    • 5 years ago
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    i am confused i just need the solution set

  37. anonymous
    • 5 years ago
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    solution is 62

  38. anonymous
    • 5 years ago
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    62 works, 2 does not

  39. anonymous
    • 5 years ago
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    ok...thx

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