Question

If by+cz/b2+c2=cz+ax/c2+a2 then prove that x/a=y/b

Answer 1

Answer:

Step-by-step explanation:

Hi,

(Some part of the question is missing, please  note it as below)

by+cz/b²+c²=cz+ax/c²+a² = ax+by/a² + b²

Let each ratio be 'k'

=>by+cz = k(b²+c²)-------(1)

cz+ax = k(c²+a²)--------(2)

ax+by = k(a² + b²)-------(3)

Adding (1) + (2) + (3) , we get

ax + by + cz = k(a² + b² + c²)------(4)

Now,

Subtracting (4) - (1), we get

ax = k(a²)

=> k = x/a------(5)

Subtracting (4)-(1), we get

by = k(b²)

=> k = y/b------(6)

Subtracting (4) - (3), we get

cz = k(c²),

=> k = z/c-----(7)

Thus, from equations (5),(6) and (7), we can conclude that

k = x/a = y/b = z/c.

Hope, it helped !

Answer 2

Answer:

Hence proved

Step-by-step explanation:

Each of the given ratio

= (by + cz) + (cz + ax) + (ax + by)/(b2 + c2) + (c2 + a2) + (a2 + b2)

= ax + by + cz/a2 + b2 + c2

Now  by + cz/b2 + c2 = ax + by + cz/a2 + b2 + c2

⇒ a2 + b2 + cz/b2 + c2  = ax + by + cz/by + cz

⇒ a2/b2 + c2  =  zx/by + cz  (App.  Dividendo)

⇒  b2 + c2/a2   = by + c2/ax  (App. Invertends)

⇒ a2 + b2 + c2/a2  =  ax + by + cz/ax    (by  componendo)

⇒  x/a = ax + by + cz/a2 + b2 + c2     (similarly)

∴      x/a = y/b = z/c  =  ax + by + cz/a2 + b2 + c2

Hence  proved