If α ,β are roots of the equation x^2+5x +5=0, then equation where roots are (α+1) and (β+1) is
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2
x
2
+5x−5=0
as we know in ax
2
+bx+c=0
a=1 b=5 C=−5
let now is α & β
α+β=
a
−b
=−5 αβ=
a
c
=−5
here
a
(α+1)
3
1
+
b
(β+1)
3
1
let α+1=a
β+1=b
so
a
3
1
+
b
3
1
(ab)
3
b
3
+a
3
(ab
3
)
(a+b)(a
2
+b
2
−ab)
(ab)
3
(a+b)[(a+b)
2
−3ab]
[(α+1)(β+1)]
3
(α+1+β+1)[(α+1)(β+1)
2
−3(α+1)(β+1)]
(αβ+α+β+1)
3
(α+β+2[(α+β+2)
2
−3(α+β+αβ+1)]
(−5−5+1)
3
(−5+2)[(−5+2)
2
−3(−5−5+1)]
(−9)
3
(−3)[(−3)
2
−3(−9)]
=
(−9)×(−9)×(−9)
36×−3
=
27
4
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