Question

X - a
If c=
find the value of x.
x-b​

Answer 1

Answer:

Let y=  

x−c

(x−a)(x−b)

​  

 

or y(x−c)=x  

2

−(a+b)x+ab

or x  

2

−(a+b+y)x+ab+cy=0

∴D=(a+b+y)  

2

−4(ab+cy)

=y  

2

+2y(a+b−2c)+(a−b)  

2

 

Since x is real and y assumes all real values we must have △≥0∀ real of y. The sign of a quadratic in y is same as of first term provided its discriminant D<0

⇒4(a+b−2c)  

2

−4(a−b)  

2

<0

⇒4(a+b−2c+a−b)(a+b−2c−a+b)<0

or 16(a−c)(b−c)<0 or 16(c−a)(c−b)=−ve

∴c lies between a and b i.e. a<c<b...(i)

where a<b but if b<a then above condition will be b<c<a or a>c>b...(ii)

Hence from (i) and (ii) we observe (d) is correct.

Step-by-step explanation: