Question

If a+b/c= b+c/ a=c+a/b=k, then the value of k is

Answer 1

Answer:

K=2

Step-by-step explanation:

Assume a=b=c=1 and substitute in the given question say,a+b/c

1+1/1 =>2 as the answer.

Try it any other number too . you will get the same answer!!

Hope it helps!!

Answer 2

K = -1

Given:

a+b/c= b+c/ a=c+a/b=k

To find:

value of k .

Solution:
(a+b)/c = (b+c)/a = (c+a)/b = k

Let's solve for k:

From the first two parts of the equation, we have:

(a+b)/c = (b+c)/a

Cross-multiplying, we get:

a(a+b) = c(b+c)

Expanding, we get:

a^2 + ab = bc + c^2

Rearranging, we get:

a^2 - c^2 = b(c - a)

Factorizing the left-hand side, we get:

(a + c)(a - c) = b(c - a)

Dividing both sides by (a - c), we get:

a + c = -b

Similarly, from the last two parts of the equation, we have:

(b+c)/a = (c+a)/b

Cross-multiplying, we get:

b(b+c) = a(c+a)

Expanding, we get:

ab + b^2 = ac + a^2

Rearranging, we get:

a^2 - ab = b^2 - bc

Factorizing the left-hand side, we get:

a(a - b) = b(c - b)

Dividing both sides by (b - a), we get:

a + b = -c

Therefore, we have:

a + b + c = 0

Substituting this value into the original equation, we get:

(a+b)/c = (b+c)/a = (c+a)/b = -(a+b+c)/(a+b+c)

Therefore, the value of k is -(a+b+c)/(a+b+c), which simplifies to -1.

Hence, k = -1.

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