If x+1/x = 3,
then what is the value of x⁵+1/x⁵ ?
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♣ ANSWER:-
Answer
x
2
−5x+1=0
∴x
2
+1=5x
∴x+
x
1
=5
∴x
2
+
x
2
1
=25−2=23
∴x
3
+
x
3
1
=(x+
x
1
)
3
−3(x+
x
1
)
∴x
3
+
x
3
1
=125−15
∴x
3
+
x
3
1
=110
Now (x
3
+
x
2
1
)(x
3
+
x
3
1
)=56×23
∴x
5
+x+
x
1
+
x
5
1
=110×23
∴x
5
+
x
5
1
=2530−5
∴x
5
+
x
5
1
=2525.
hopefully it helps
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