If alpha and bita are the roots of the equation x square +3 x-2 =0 then alpha square bita + alpha bita square equals to?
Answers
Answered by
1
α and β are roots of the given equation x
2
+3x−2=0
Here, a=1,b=3,c=−2
⇒ αβ=
a
c
=
1
−2
=−2 ---- ( 1 )
⇒ α+β=
a
−b
=
1
−3
=−3 ----- ( 2 )
⇒ (α+β)
2
=α
2
+β
2
+2αβ
⇒ (−3)
2
=αβ
2
+2(−2) [ Using ( 1 ) and ( 2 ) ]
⇒ 9=α
2
+β
2
−4
∴ α
2
+β
2
=13 ---- ( 3 )
β
α+1
+
α
β+1
=
αβ
α
2
+α+β
2
+β
=
αβ
α
2
+β
2
+α+β
=
−2
13−3
[ From ( 1 ), ( 2 ) and ( 3 ) ]
=
2
−10
=−5
∴
β
α+1
+
α
β+1
=−5
Similar questions