Question

X/b+c-a=y/c+a-b=z/a+b+c show that x+y+z/a+b+c

Answer 1

Solution :

• Given : x/(b+c-a) = y/(c+a-b) = z(a+b-c)

• To prove : (x + y + z)/(a + b + c) = k (constant)

Let ,

x/(b+c-a) = y/(c+a-b) = z(a+b-c) = k (constant)

• x/(b+c-a) = k

=> x = k(b + c - a)

• y/(c+a-b) = k

=> y = k(c + a - b)

• z(a+b-c) = k

=> z = k(a + b - c)

Now ,

=> x+y+z = k(b+c-a) + k(c+a-b) + k(a+b-c)

=> x+y+z = k(b + c - a + c + a - b + a + b - c)

=> x + y + z = k(a + b + c)

=> (x + y + z) / (a + b + c) = k

Hence proved .