If (x+1/x)=4,find the values of :(i) (x^3+1/x^3) (ii)(x-1/x) (iii) (x^3-1/x^3)
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Answer:
If x
4
+
x
4
1
=6239, find x+
x
1
.
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x
4
+
x
4
1
=6239
⇒(x
2
+
x
2
1
)
2
−2=6239
⇒x
2
+
x
2
1
=
6239+2
⇒x
2
+
x
2
1
=
6241
=79
⇒(x+
x
1
)
2
−2=79
⇒x+
x
1
=
79+2
=
81
=9
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