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# How to

How to do the following:

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

Note by Syed Baqir
2 years ago

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From 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. · 2 years ago

nice solution · 2 years ago