anonymous
  • anonymous
Given that c (ax + by - cz) = b (ax - by + cz) = a ( -ax + by + cz) = 2 then ax + by + cz/ab + bc + ca = ?
Mathematics
schrodinger
  • schrodinger
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perl
  • perl
Let's unpack the first statement. c (ax + by - cz) = b (ax - by + cz) = a ( -ax + by + cz) = 2
perl
  • perl
If we look at the first two statements c (ax + by - cz) = 2 b (ax - by + cz) = 2 It follows that (ax + by - cz) = 2/c (ax - by + cz) = 2/b now you can add these two equations to eliminate variables x and y 2ax = 2/c + 2/b
perl
  • perl
can you solve that for x ?

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anonymous
  • anonymous
Yes. How do we exactly approach such questions? Is there any trick?
perl
  • perl
What I wrote is clear so far?
anonymous
  • anonymous
x = 1/ac + 1/ab
anonymous
  • anonymous
Okay
perl
  • perl
The approach I used is common to solving linear equations, try to find a way to eliminate a variable. Well not exactly this approach, after some work
perl
  • perl
lets be more careful with solving for x
perl
  • perl
2ax = 2/c + 2/b you divided out 2 correctly ax = 1/c + 1/b first simplify 1/c + 1/b ax = ( b + c ) / (bc) now divide by a x = ( b + c ) / (abc)
perl
  • perl
$$ \large \frac{1}{b} + \frac{1}{c} = \frac{1}{b}\cdot \frac {c}{c} + \frac{1}{c} \cdot \frac{b}{b}= \frac{c}{bc} + \frac{b}{bc} = \frac{b+c}{bc}$$
anonymous
  • anonymous
Thank you @perl

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