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JEE Main 24 June 2022 Shift 1 Solved Paper
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© examsnet.com
Question : 7
Total: 90
If the sum of the squares of the reciprocals of the roots
α
and
β
of the equation
3
x
2
+
λ
x
−
1
=
0
is 15 , then
6
(
α
3
+
β
3
)
2
is equal to:
[24-Jun-2022-Shift-1]
18
24
36
96
Validate
Solution:
👈: Video Solution
3
x
2
+
λ
x
−
1
=
0
Given, two roots are
α
and
β
.
∴
Sum of roots
=
α
+
β
=
−
λ
3
And product of roots
=
α
β
=
−
1
3
Given that,
Sum of square of reciprocal of roots
α
and
β
is 15 .
∴
1
α
2
+
1
β
2
=
15
⇒
α
2
+
β
2
α
2
β
2
=
15
⇒
(
α
+
β
)
2
−
2
α
β
(
α
β
)
2
=
15
⇒
λ
2
9
+
2
×
1
3
1
9
=
15
⇒
λ
2
+
6
9
1
9
=
15
⇒
λ
2
+
6
=
15
⇒
λ
2
=
9
Now,
6
(
α
3
+
β
3
)
2
=
6
{
(
α
+
β
)
(
α
2
+
β
2
−
α
β
)
}
2
=
6
(
α
+
β
)
2
[
(
α
+
β
)
2
−
2
α
β
−
α
β
]
2
=
6
(
−
λ
3
)
2
[
(
−
λ
3
)
2
−
3
⋅
−
1
3
]
2
=
6
×
λ
2
9
×
[
λ
2
9
+
1
]
=
6
×
9
9
×
[
9
9
+
1
]
2
=
6
×
(
2
)
2
=
6
×
4
=
24
© examsnet.com
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