Question

If a/(x-2y+3z) = b/(y-2z+3x) = c/(z-2x+3y) and x+y+z ≠ 0, then prove that each ratio = a+b+c/2(x+y+z)

Answer 1

Answer:

k

Step-by-step explanation:

let a\(x-2y+3z) = b\(y-2z+3x) = c\(z-2x+3y)

.:. by theorem of equal ratios

k= a+b+c

--------------------------------------------

( x-2y+3z) + (y-2z+3x) + (z-2x+3y)

= a + b + c

-----------------

2x+2y+2z

= a + b + c

-----------------

2(x+y+z)

.:. a. b c

--------------- = ------------------- = -----------------

x-2y+3z y-2z+3z z-2x+3y

= a + b + c

------------------

2(x+y+z)