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 } } $

#1 #3 #2 #5 #4

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

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

Vishnu Bhagyanath - 5 years, 9 months ago

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.

คลุง แจ็ค - 5 years, 9 months ago

nice solution

Syed Baqir - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$