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Please help me in this olympiad question

  1. Mar 14, 2013 #1
    (x,y,z)∈R^3 are points that lie on the plane x+2y+3z=78, and lie on the sphere x^2+y^2+z^2=468. The maximum value of x has the form a/b, where a and b are coprime positive integers. What is the value of a+b?
     
  2. jcsd
  3. Mar 14, 2013 #2

    mfb

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    Here is a hint: How does the intersection of a plane and a sphere look like?
    Once you know the maximum value of x, calculating a+b should be easy.
     
  4. Mar 14, 2013 #3
    hello friend, i even dont know from which topic is this question,help?

    i even dont know from which topic is this question,please help?
     
    Last edited: Mar 14, 2013
  5. Mar 14, 2013 #4
    So can anyone give me its complete solution,?

    so that I can understand the concept.
     
  6. Mar 14, 2013 #5

    HallsofIvy

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    Can you first answer mfb's question? What does the intersection of a sphere and a plane look like? What kind of figure is that?

    You can find the equation of that graph by solving the two equations, x+2y+3z=78, and [itex]x^2+y^2+z^2=468[/itex] simultaneously. Since that is two equations in three variables, you can solve for two, say x and y, in terms of the third.
     
    Last edited: Mar 14, 2013
  7. Mar 14, 2013 #6
    I think it would be a circle.Please check whether I am correct or not.......
     
  8. Mar 14, 2013 #7

    mfb

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    It is a circle, right.
     
  9. Mar 14, 2013 #8
    then what to do, you guys just tell me the steps I will do all by my own,so what will be the next step?
     
  10. Mar 14, 2013 #9
    then i think we have to find the radius of this circle....am i correct.....?
     
  11. Mar 14, 2013 #10

    mfb

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    That is possible. I used a different approach, but there are many ways to solve this.

    Can you link the source of the question? If it is not a current question, I might give more hints.
     
  12. Mar 14, 2013 #11
    yes give me hints...
     
  13. Mar 14, 2013 #12
    I think the radius is 5.78, and that is not the answer.....help!!!
     
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