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Math Help - ex.algebra..

  1. #1
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    ex.algebra..

    Hello!!!
    I am new in this forum, and it seems really interesting !
    Could you help me with some exercises? I would be grateful !

    1) f: R -> R , f(x)=(x-1)(x-2)(x-3)(x-4) , then f(R)=...?
    // R=the multitude of real numbers

    2) if p is a natural and prime number and A={ k nr. integer, | sqrt(k*k-p*k)
    is a natural number } , then the number of elements of A is .....?

    3) If M={ m integer nr. | (m*m*m-3*m+2)/(2*m+1) is an integer nr.} , then the minimum and the maximum from M are ....?

    Thank you very much!!!!
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  2. #2
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    Quote Originally Posted by inzaghina View Post
    1) f: R -> R , f(x)=(x-1)(x-2)(x-3)(x-4) , then f(R)=...?
    // R=the multitude of real numbers
    (x-1)(x-2)(x-3)(x-4)=[(x-1)(x-4)][(x-2)(x-3)] = (x^2-5x+4)(x^2-5x+6)
    [(x^2-5x+5)-1][(x^2-5x+5)+1] = (x^2-5x+5)^2 - 1
    For the equation, (x^2-5x+5)^2 - 1 = y \implies (x^2-5x+5)^2 = y+1 to have a solution it means, y+1\geq 0 then x^2-5x+5 = \sqrt{y-1}. Now for this equation to have a solution we require that 25 - 4(5-\sqrt{y-1}) \geq 0. Solve for y.

    Can you explain the other prolems?
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