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Byju's Answer
Standard XII
Mathematics
Quadratic Polynomial
If x2-x+1=0 t...
Question
If
x
2
−
x
+
1
=
0
then the value of
(
x
+
1
x
)
2
+
(
x
2
+
1
x
2
)
2
+
(
x
3
+
1
x
3
)
2
+
(
x
5
+
1
x
5
)
2
is
Open in App
Solution
Given :
x
2
−
x
+
1
=
0
⇒
x
+
1
x
=
1
⇒
x
2
+
1
x
2
+
2
=
1
⇒
x
2
+
1
x
2
=
−
1
Cubing
x
+
1
x
=
1
, we get
x
3
+
1
x
3
+
3
(
x
+
1
x
)
=
1
⇒
x
3
+
1
x
3
=
−
2
Also,
(
x
2
+
1
x
2
)
⋅
(
x
3
+
1
x
3
)
=
x
5
+
1
x
5
+
x
+
1
x
⇒
2
=
x
5
+
1
x
5
+
1
⇒
x
5
+
1
x
5
=
1
Therefore,
(
x
+
1
x
)
2
+
(
x
2
+
1
x
2
)
2
+
(
x
3
+
1
x
3
)
2
+
(
x
5
+
1
x
5
)
2
=
1
2
+
(
−
1
)
2
+
(
−
2
)
2
+
1
2
=
7
Suggest Corrections
3
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Q.
If
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Q.
For constant of integration
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∫
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3
+
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+
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then
Q.
If
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,
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are the roots of the equation
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−
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x
+
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=
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and
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1
,
β
1
be the roots of the equation
x
2
−
q
x
+
p
=
0
, then form the quadratic equation whose roots are
1
α
1
β
+
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β
1
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Q.
If
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then the value of
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