if à, b are the roots of the equation ax²+bx+c=0,then the value of 1/aa+b+1/ab+b
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If α,β are roots of equation ax
2
+bx+c=0 then α+β=
a
−b
&αβ=
a
c
i) (1+α)(1+β)
=1+α+β+αβ
=1+(
a
−b
)+
a
c
=1+(
a
c−b
)
ii) α
3
β+αβ
3
αβ(α
2
+β
2
)
a
c
(
a
2
b
2
−
a
2c
)
a
3
c
(b
2
−2ac)
α+β=−
a
b
(α+β)
2
=b
2
/a
2
α
2
+β
2
+2αβ=b
2
/a
2
α
2
+β
2
=
a
2
b
2
−
a
2c
iii)
α
1
+
β
1
αβ
β
+
αβ
α
=
αβ
β+α
=
a
−b
×
c
a
=
c
−b
iv)
aα+b
1
+
aβ+b
1
α+β=
a
−b
=
aα−a(α+β)
1
+
aβ−a(α+β)
1
⇒b=−a(α+β)
=
aα−aα−aβ
1
+
aβ−aα−aβ
1
=−
a
1
(
α
1
+
β
1
)=
a
−1
(
c
−b
)=
ac
b
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