## 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 = ?

1. perl

Let's unpack the first statement. c (ax + by - cz) = b (ax - by + cz) = a ( -ax + by + cz) = 2

2. 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

3. perl

can you solve that for x ?

4. anonymous

Yes. How do we exactly approach such questions? Is there any trick?

5. perl

What I wrote is clear so far?

6. anonymous

x = 1/ac + 1/ab

7. anonymous

Okay

8. 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

9. perl

lets be more careful with solving for x

10. 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)

11. perl

$$\large \frac{1}{b} + \frac{1}{c} = \frac{1}{b}\cdot \frac {c}{c} + \frac{1}{c} \cdot \frac{b}{b}= \frac{c}{bc} + \frac{b}{bc} = \frac{b+c}{bc}$$

12. anonymous

Thank you @perl