How to do the following:

\(if\quad x\quad =\quad cy\quad +\quad bz\\ \quad \quad \quad y\quad =\quad az\quad +\quad cx\\ \quad \quad \quad z\quad =\quad bx\quad +\quad ay\\ \\ then\quad show\quad that\quad :\quad \frac { { x }^{ 2 } }{ 1-{ a }^{ 2 } } =\frac { { y }^{ 2 } }{ 1-{ b }^{ 2 } } =\frac { { z }^{ 2 } }{ 1-{ c }^{ 2 } } \)

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## Comments

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TopNewestFrom equation for y and z we have

\( x=\dfrac{y-az}{c}=\dfrac{z-ay}{b} \)

\( cy+bz=\dfrac{y-az}{c} \) then \( (a+bc)z=(1-c^{2})y --(1)\)

\( cy+bz=\dfrac{z-ay}{b} \) then \( (a+bc)y=(1-b^{2})z --(2)\)

\( (1)\div (2)=\dfrac{z}{y}=\dfrac{(1-c^{2})y}{(1-b^{2})z} \)

Thus \( \dfrac{y^{2}}{1-b^{2}}=\dfrac{z^{2}}{1-c^{2}} \) then do the same for x and a you will get what are you seeking for.

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nice solution

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Kindly show us your attempt at the answer and where you're getting stuck.

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