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Math Help - algebra help

  1. #1
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    algebra help

    an equation is shown.

    [the square root of (x2-t2)] = 2t-x

    If x and t are positive numbers that satisfy the equation above, what is the value of (x/t)?
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  2. #2
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    Re: algebra help

    Quote Originally Posted by Mat724 View Post
    [the square root of (x2-t2)] = 2t-x

    If x and t are positive numbers that satisfy the equation above, what is the value of (x/t)?
    \sqrt{x^2-t^2}=2t-x

    \Rightarrow x^2-t^2 = 4t^2-4tx+x^2

    \Rightarrow 5t^2-4tx = 0

    \Rightarrow t(5t - 4x) = 0

    t > 0, so

    5t-4x = 0\quad\Rightarrow\quad4x=5t\quad\Rightarrow\quad \frac xt=\frac54
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  3. #3
    Senior Member DeMath's Avatar
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    Re: algebra help

    Hint

    \begin{gathered} \sqrt {{x^2} - {t^2}}  = 2t - x \hfill \\ t\sqrt {{{\left( {\frac{x}{t}} \right)}^2} - 1}  = 2t - x \hfill \\ \sqrt {{{\left( {\frac{x}{t}} \right)}^2} - 1}  = 2 - \frac{x}{t} \hfill \\ \text{Let}\,\frac{x}{t} = a,\quad\text{domain}\colon\,|a| \geqslant 1 \hfill \\ \sqrt {{a^2} - 1}  = 2 - a \hfill \\ {a^2} - 1 = {(2 - a)^2} \hfill \\{a^2} - 1 = 4 - 4a + {a^2} \hfill \\ 4a = 5 \hfill \\ a = \frac{5}{4} \hfill \\ \end{gathered}
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