Question

(a2b+ab2)÷ab Find the quotient

Answer 1

Answer:

A=a

2

b+ab

2

−a

2

c−ac

2

=a(b−c)(a+b+c)

B=b

2

c+bc

2

−a

2

b−ab

2

=b(c−a)(a+b+c), and

C=a

2

c+ac

2

−b

2

c−bc

2

=c(a−b)(a+b+c)

.

If Ax

2

+Bx+C=0 has equal roots, then

B

2

−4AC=0

b

2

(c−a)

2

=4ac(b−c)(a−b)

b

2

(a

2

−2ac+c

2

)=4ac(ab+bc−ac−b

2

)

a

2

b

2

−2ab

2

c+b

2

c

2

=4a

2

bc+4abc

2

−4a

2

c

2

−4ab

2

c

Simplify to get,

(ab−2ac+bc)

2

=0

ab+bc=2ac

Dividing by abc

a

1

+

c

1

=

b

2

∴ a,b,c are in H.P.

I hope it's helpful ☺️