if alpha and bita are the roots of equation x²-2x+3=0,then find the equation whose roots are (alpha+2) and (bita+2)
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Let α,β are roots of x
2
−2x+3=0
Then α+β=2;αβ=3.
Now
α+1
α−1
+
β+1
β−1
=
(α+1)(β+1)
(α−1)(β+1)+(α+1)(β−1)
=
αβ+α+β+1
αβ+α−β−1+αβ−α+β−1
=
αβ+α+β+1
2αβ−2
=
3+2+1
6−2
=
6
4
=
3
2
(
α+1
α−1
)(
β+1
β−1
)=
(αβ+α+β+1)
αβ−α−β+1
=
3+2+1
3−2+1
=
6
2
=
3
1
Hence, equation is x
2
−(
3
2
)x+(
3
1
)=0⇒3x
2
−2x+1=0.
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