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 August 26th, 2014, 06:20 AM #1 Senior Member   Joined: Nov 2013 Posts: 434 Thanks: 8 Given conditions, prove the following
 August 26th, 2014, 07:16 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 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.
August 26th, 2014, 01:00 PM   #3
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Quote:
 Originally Posted by mared
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).

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 $\displaystyle \text{If }x=cy+bz,\ y=az+cx,\ z=bx+ay \\ \text{show that}\displaystyle \frac{x^2}{1-a^2} = \frac{y^2}{1-b^2} = \frac{z^2}{1-c^2}$
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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