Question

value of k could be:
a)a+b
b)b+c
c)a-b
d)b-c
answer with explaination and get branliest​

Answer 1

Question : -

If (a²+c²)/(a+c) = (b²+c²)/(b+c) = k and a ≠ b, then the value of k ?

• a) a+b
• b) b+c
• c) a-b
• d) b-c

ANSWER

Given : -

(a²+c²)/(a+c) = (b²+c²)/(b+c) = k & a≠b

Required to find : -

• Value of k ?

Solution : -

Given that;

(a²+c²)/(a+c) = (b²+c²)/(b+c) = k & a≠b

So,

(a²+c²)/(a+c) = k & (b²+c²)/(b+c) = k

We have,

(a²+c²)/(a+c) = k

a²+c² = k(a+c)

a²+c² = ak+ck

a²+c²-ak-ck = 0 .... (1)

Similarly,

(b²+c²)/(b+c) = k

b²+c² = k(b+c)

b²+c² = bk+ck

b²+c²-bk-ck = 0 ... (2)

From (1)&(2) we have,

a²+c²-ak-ck = b²+c²-bk-ck

cancelling the like terms on both sides

a²-ak = b²-bk

a²-b² = ak-bk

since,

• a²-b² = (a+b) (a-b)

(a+b) (a-b) = k(a-b)

cancelling (a-b) on both sides

(a+b) = k

Therefore,

Value of k = (a+b) ✓

Hence, option-A is correct ....

Answer 2

$\huge\mathfrak{Question}$

If (a²+c²)/(a+c) = (b²+c²)/(b+c) = k and a ≠ b, then the value of k ?

a) a+b

b) b+c

c) a-b

d) b-c

ANSWER :-

Given : -

(a²+c²)/(a+c) = (b²+c²)/(b+c) = k & a≠b

Required to find : -

Value of k ?

Solution : -

Given that;

(a²+c²)/(a+c) = (b²+c²)/(b+c) = k & a≠b

So,

(a²+c²)/(a+c) = k & (b²+c²)/(b+c) = k

We have,

(a²+c²)/(a+c) = k

a²+c² = k(a+c)

a²+c² = ak+ck

a²+c²-ak-ck = 0 .... (1)

Similarly,

(b²+c²)/(b+c) = k

b²+c² = k(b+c)

b²+c² = bk+ck

b²+c²-bk-ck = 0 ... (2)

From (1)&(2) we have,

a²+c²-ak-ck = b²+c²-bk-ck

cancelling the like terms on both sides

a²-ak = b²-bk

a²-b² = ak-bk

since,

a²-b² = (a+b) (a-b)

(a+b) (a-b) = k(a-b)

cancelling (a-b) on both sides

(a+b) = k

Therefore,

Value of k = (a+b) ✓

Hence, option-A is correct