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August 26th, 2014, 06:20 AM   #1
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Given conditions, prove the following

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August 26th, 2014, 07:16 AM   #2
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Please take more care in giving your threads titles. You post problem after problem with no effort ever shown, the least you can do is give your threads descriptive titles.
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August 26th, 2014, 01:00 PM   #3
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Quote:
Originally Posted by mared View Post
Ths may not be what you had in mind, but you have three linear equations in three unknowns. The system is satisfied by x=y=z=0, so the question you are asking is trivial (each term is 0).
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August 26th, 2014, 01:23 PM   #4
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That's incorrect, as x = y = z = 0 isn't the only possibility.

Quote:
Originally Posted by mared View Post
$\displaystyle \text{If }x=cy+bz,\ y=az+cx,\ z=bx+ay \\
\text{show that}\displaystyle \frac{x^2}{1-a^2} = \frac{y^2}{1-b^2} = \frac{z^2}{1-c^2}$
x² = x(cy + b(bx + ay)) = cxy + b²x² + abxy.
y² = y(a(bx + ay) + cx) = abxy + a²y² + cxy.
By subtraction, x²(1 - b²) = y²(1 - a²).
Similarly, y²(1 - c²) = z²(1 - b²).
If a², b² and c² all differ from 1, the required result follows.

Last edited by skipjack; August 26th, 2014 at 02:46 PM.
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