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anonymous

  • one year ago

Given that c (ax + by - cz) = b (ax - by + cz) = a ( -ax + by + cz) = 2 then ax + by + cz/ab + bc + ca = ?

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  1. perl
    • one year ago
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    Let's unpack the first statement. c (ax + by - cz) = b (ax - by + cz) = a ( -ax + by + cz) = 2

  2. perl
    • one year ago
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    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

  3. perl
    • one year ago
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    can you solve that for x ?

  4. anonymous
    • one year ago
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    Yes. How do we exactly approach such questions? Is there any trick?

  5. perl
    • one year ago
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    What I wrote is clear so far?

  6. anonymous
    • one year ago
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    x = 1/ac + 1/ab

  7. anonymous
    • one year ago
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    Okay

  8. perl
    • one year ago
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    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

  9. perl
    • one year ago
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    lets be more careful with solving for x

  10. perl
    • one year ago
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    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)

  11. perl
    • one year ago
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    $$ \large \frac{1}{b} + \frac{1}{c} = \frac{1}{b}\cdot \frac {c}{c} + \frac{1}{c} \cdot \frac{b}{b}= \frac{c}{bc} + \frac{b}{bc} = \frac{b+c}{bc}$$

  12. anonymous
    • one year ago
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    Thank you @perl

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