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Math Help - Is this right MK2

  1. #1
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    Is this right MK2

    Hi guys,
    Got this bit right.......... thanks for the conformation

    (a) Expand ( x + ⅟x ) = x + 2x⅟x + ⅟x₂ = x + 2 + ⅟x₂
    (b) Suppose that x + ⅟x = 3. Use part (a) to evaluate x + ⅟x without attempting to find the value of x.
    ok my thoughts are..... ( x + ⅟x ) = (3) from above.
    so i think i should use the solution x + 2 + ⅟x₂ which would be 9 + 2.
    The question asks me to evaluate, but I think I may be on the wrong track. as I feel I am solving for x.

    Am I doing the wrong thing here?
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  2. #2
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    Quote Originally Posted by Joel View Post
    Hi guys,
    Got this bit right.......... thanks for the conformation

    (a) Expand ( x + ⅟x ) = x + 2x⅟x + ⅟x₂ = x + 2 + ⅟x₂
    (b) Suppose that x + ⅟x = 3. Use part (a) to evaluate x + ⅟x without attempting to find the value of x.
    ok my thoughts are..... ( x + ⅟x ) = (3) from above.
    so i think i should use the solution x + 2 + ⅟x₂ which would be 9 + 2.
    The question asks me to evaluate, but I think I may be on the wrong track. as I feel I am solving for x.

    Am I doing the wrong thing here?
    \left(x + \frac{1}{x}\right)^2 = x^2 + 2 + \frac{1}{x^2}.


    If x + \frac{1}{x} = 3, then \left(x + \frac{1}{x}\right)^2 = 3^2 = 9.


    Thus x^2 + 2 + \frac{1}{x^2} = 9

    And so x^2 + \frac{1}{x^2} = 7.
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  3. #3
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    Quote Originally Posted by Joel View Post
    Hi guys,
    Got this bit right.......... thanks for the conformation

    (a) Expand ( x + ⅟x ) = x + 2x⅟x + ⅟x₂ = x + 2 + ⅟x₂
    (b) Suppose that x + ⅟x = 3. Use part (a) to evaluate x + ⅟x without attempting to find the value of x.
    ok my thoughts are..... ( x + ⅟x ) = (3) from above.
    so i think i should use the solution x + 2 + ⅟x₂ which would be 9 + 2.
    The question asks me to evaluate, but I think I may be on the wrong track. as I feel I am solving for x.

    Am I doing the wrong thing here?
    Hi Joel,

    (a) Expand \left(x+\frac{1}{x}\right)^2


    \left(x+\frac{1}{x}\right)^2=x^2+2+\frac{1}{x^2}

    (b) Suppose x+\frac{1}{x}=3

    Use part (a) to evaluate x^2+\frac{1}{x^2} without attempting to find the value of x.

    x + \frac{1}{x}=3

    \left(x+\frac{1}{x}\right)^2=9

    x^2+\frac{1}{x^2}+2=9

    x^2+\frac{1}{x^2}=7

    Edit: Too slow......Prove it got there first. Rats!
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  4. #4
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    Ok Thanks heaps guys,

    I was on the right track but looking at your solutions, I was going about the last step by solving it rather than representing it via x.

    Cheers
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