Question

(c²-ab)x²-2(a²-bc)x+b²-ac=0​

Answer 1

ANSWER

(c

2

=ab)x

2

−2(a

2

−bc)x+(b

2

−ac)=0

comparing with Ax

2

+Bx+C=0, we get

∴A=(c

2

−ab),B=−2(a

2

−bc),C=(b

2

−ac)

Roots of the quadratic eqn. are equal

⇒D=0

⇒

B

2

−4AC

=0

⇒B

2

−4AC=0

⇒B

2

=4AC

⇒[−2(a

2

−bc)

2

]=4(c

2

−ab)(b

2

−ac)

⇒4(a

2

−bc)

2

=4(c

2

−ab)(b

2

−ac)

⇒a

4

+b

2

c

2

−2a

2

bc=b

2

c

2

−ac

3

−ab

3

+a

2

bc

⇒a

4

+ab

3

+ac

3

=3a

2

bc.

⇒a(a

3

+b

3

+c

3

−3abc)=0.

∴a=oora

3

+b

3

+c

3

=3abc.

Answer 2

Please refer to the Attachment