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Math Help - Prove the ratio

  1. #1
    Member kalyanram's Avatar
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    Prove the ratio

    Please prove this...
    Given
    x = cy+bz, y = az+cx, z = bx+ay ; show that \frac{x^2}{1-a^2} = \frac{y^2}{1-b^2} = \frac{z^2}{1-c^2}

    ~Kalyan
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by kalyanram View Post
    Please prove this...
    Given
    x = cy+bz, y = az+cx, z = bx+ay ; show that \frac{x^2}{1-{a^2}} = \frac{y^2}{1-{b^2}} = \frac{z^2}{1-{c^2}}

    ~Kalyan
    The syntax is \frac{...}{...}
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  3. #3
    Lord of certain Rings
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    Quote Originally Posted by kalyanram View Post
    Please prove this...
    Given
    x = cy+bz, y = az+cx, z = bx+ay ; show that \frac{x^2}{1-a^2} = \frac{y^2}{1-b^2} = \frac{z^2}{1-c^2}

    ~Kalyan
    y = az+cx \Rightarrow  y = az+c(cy+bz) = az +cbz + c^2y \Rightarrow y(1 - c^2) = (a+bc)z-----------(1)

    z = bx+ay = b(cy+bz) + ay = (bc+a)y+ zb^2 \Rightarrow z(1-b^2) = (a+bc)y----------------------(2)

    Divide (1) by (2), to get \frac{y(1-c^2)}{z(1- b^2)} = \frac{z}{y} \Rightarrow \frac{y^2}{1- b^2} = \frac{z^2}{1 - c^2}

    You can similarly prove the other ratio by eliminating y(or z) in both the equations.
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