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Math Help - Challenging quadratic questions

  1. #1
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    Challenging quadratic questions

    I'm sorry I haven't got any ideas down, but I really don't have any clue as to how to solve these. [FONT=Arial][SIZE=2]Please help me with the following questions:

    1) Find all real numbers x such that x^8+x^4+x^2+2x+1 is less than or equal to 2x^6. Show all the working details.




    2) If the linear graph of y=x+1 passes through the turning pointof the quadratic graph given by the rule y=x^2 + 2(m+1)x - m+1, find all the possible values of m. Show all the working details.




    3) Rpove that the equation (x^2) +(y^2)-(z^2) = 1997 has infinitely many solutions in integers x, y and z. Show all the working details.
    Last edited by ibeatboris; September 2nd 2009 at 04:18 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ibeatboris View Post
    I'm sorry I haven't got any ideas down, but I really don't have any clue as to how to solve these. Please help me with the following questions:

    1) Find all real numbers x such that x
    +x +x +2x+1 ≤ 2x ⁶. Show all the working details.
    Do not use unusual charaters, they do not render on everyones computers. For powers use ^, so x squared would be written x^2, cubed x^3, etc.

    CB
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