if x+1/x=5 then the value of x3-1/x3
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Answer:
Given, x−
x
1
=5
Squaring both the sides,
⇒(x−
x
1
)
2
=5
2
⇒x
2
+
x
2
1
−2(x)(
x
1
)=25
⇒x
2
+
x
2
1
=25+2
⇒x
2
+
x
2
1
=27
Now,
x
3
−
x
3
1
=(x−
x
1
)[(x)
2
+(
x
1
)
2
+(x)(
x
1
)]
=5(27+1)
=140
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