Question

Prove that both the roots of the equation (x – a)(x – b)+(x – b)(x – c) + (x –

(x – a) = 0 are real but they are equal only when a = b = c


Solve this
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Answer 1

Step-by-step explanation:

A= B = C ✅

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Answer 2

3x

2

−2x(a+b+c)+(ab+bc+ca)=0

Let D be the discriminant

D=4(a+b+c)

2

−12(ab+bc+ca)

=4[(a+b+c)

2

−3(ab+bc+ca)]

=2[2a

2

+2b

2

+2c

2

−2ab−2bc−2ca]

=2[(a−b)

2

+(b−c)

2

+(c−a)

2

]

If D=0, then

(a−b)

2

+(b−c)

2

+(c−a)

2

=0

⇒a−b=0;b=c;c=a

or a=b=c