if x^2+1/x=3 1/3 then what is the value of x^3-1/x^3
Answers
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Step-by-step explanation:
Since (a−
a
1
)
3
=a
3
−
a
3
1
−3(a−
a
1
), therefore, consider (x−
x
1
)
3
and solve:
(x−
x
1
)
3
=x
3
−
x
3
1
−3(x−
x
1
)
⇒(x−
x
1
)
3
=(x
3
−
x
3
1
)−3(x−
x
1
)
⇒(x
3
−
x
3
1
)=(x−
x
1
)
3
+3(x−
x
1
)
It is given that x−
x
1
=3, therefore,
x
3
−
x
3
1
=(3)
3
+3(3)=27+9=36
Hence, x
3
−
x
3
1
=36.
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