Question

if x minus a into x minus b plus x minus b into x minus c plus x minus c plus x minus a is equal to 0 and a minus b is qual to c then find x​

Answer 1

Answer:

(X-A) × (X-B)+(X-B) × (X-C) + (X-C) × (X-A) =0

X2-BX-AX+AB+X2-CX-BX+BC+X2-AX-CX+CA=0

3X2-2AX-2BX-2CX+AB+BC+CA=0

3X2-2X(A+B+C)+AB+BC+CA=0

Sum of the roots =- b/a

=-(-2(A+B+C))/3

=2(A+B+C)/3

product of the roots=c/a=AB+BC+CA/3

Answer 2

Answer:

x = 0 or x =  (2ab - ac - bc)/(a + b - 2c).

Step-by-step explanation:

Hi,

Given a/(x - a) + b/(x - b) = 2c/( x - c)

On adding 2 on both sides, we get

a/(x - a) + 1 + b/(x - b) + 1 = 2c/(x - c) + 2

On simplifying , we get

x/( x - a) + x/( x - b) = 2x/(x - c)

x/( x - a) + x/( x - b) - 2x/(x - c) = 0

Taking x common out we get

x[ 1/ x-a + 1/x-b - 2/x-c] = 0

Hence either x = 0 or

1/ x-a + 1/x-b - 2/x-c = 0

1/ x-a + 1/x-b =  2/x-c

(2x - (a+b))(x -c) = 2(x-a)(x-b)

2x² -x(2c + a + b) + c(a + b) = 2(x² -x(a + b) + ab)

(a + b - 2c)x = 2ab - ac - bc

x = (2ab - ac - bc)/(a + b - 2c).

Hence, solutions are x = 0 or x =  (2ab - ac - bc)/(a + b - 2c).

Hope, it helps !