Mathematics

Question

A number is four times larger then the square of half the number

2 Answer

  • I think its -2, and hope this was helpful (:
  • n is 4 more than square of half of n

    [tex]n=4+ (\frac{n}{2})^2[/tex]
    [tex]n=4+ \frac{n^2}{4}[/tex]
    times both sides by 4
    4n=16+n²
    minus 4n both sides
    0=n²-4n+16
    gots to use quadratic formula
    for an²+bn+c=0
    n=[tex] \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
    1n²-4n+16=0

    n=[tex] \frac{-(-4)+/- \sqrt{(-4)^2-4(1)(16)} }{2(1)} [/tex]
    n=[tex] \frac{4+/- \sqrt{16-64} }{2} [/tex]
    n=[tex] \frac{4+/- \sqrt{-48} }{2} [/tex]
    uh oh, we got imaginary numbers
    if we simplify we get n=2+2i√3 or n=2-2i√3

    that can't be right



    maybe it's
    [tex]n=4+\frac{n^2}{2}[/tex]
    times both side sby 2
    2n=8+n²
    minus 2n

    0=n²-2n+8
    factor
    0=(n-4)(n+2)
    st to zero

    n-4=0
    n=4

    n+2=0
    n=-2


    the number is -2 or 4










    if it be [tex]n=4+ (\frac{n}{2})^2[/tex] then n=2+2i√3 or 2-2i√3
    if it be [tex]n=4+ \frac{n^2}{2}[/tex] then n=-2 or 4
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