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Kurosaki Akatsu Coordinator

09/03/2017 at 21:31
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Give \(P=\dfrac{ax^{2\:}+bx+c}{a'x^2+b'x+c'}\)

Demonstrate if \(\dfrac{a}{a'}=\dfrac{b}{b'}=\dfrac{c}{c'}\) then P does not depend on x

 




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    mathlove 09/03/2017 at 22:26

    Set  \(\dfrac{a}{a'}=\dfrac{b}{b'}=\dfrac{c}{c'}=k\). We have ​ ​​ ​\(k=\dfrac{ax^2}{a'x^2}=\dfrac{bx}{b'x}=\dfrac{c}{c'}=\dfrac{ax^2+bx+c}{a'x^2+b'x+c}=P\).

    So that \(P=k,\forall x\) . So \(P\) does  not depend on \(x\) .

    Kurosaki Akatsu selected this answer.
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    FA FIFA Club World Cup 2018 16/01/2018 at 21:58

    Set  aa′=bb′=cc′=k. We have ​ ​​ ​k=ax2a′x2=bxb′x=cc′=ax2+bx+ca′x2+b′x+c=P

    .

    So that P=k,∀x

     . So P does  not depend on x .


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