AP EAMCET Engineering 23 Apr 2019 Shift 1 Paper

Consider the expression,
r1=

Δ

s−a

=36
Similarly,
r2=

Δ

s−b

=18
r3=

Δ

s−c

=12
Then,

1

r12

+

1

r22

+

1

r32

+

1

r2

=

1

36

+

1

18

+

1

12

=

1+2+3

36

=

1

6

This implies,

s−a+s−b+s−c

Δ

=

1

6

s

Δ

=

1

6

Δ=6s
So,

6s

s−a

=36
s=6s−6a
6a=5c
And,

6s

s−b

=16
s=3s−3b
3b=2c
And,

6s

s−c

=12
s=2s−2c
2c=s
So,
Δ2=36s2
Then,
s(s−a)(s−b)(s−c)=36s2
(s−

5s

6

) (s−

2s

3

)(s−

s

2

)=36s
s3(

1

6

)(

1

3

)(

1

2

)=36s
s=36
So,
a=30
b=4
This implies,
a+b=30+24
=54