if ( x + 1 / x ) = 4 / 3 , find ( x cube + 1 / x cube ) = ?
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Given, x+
x
1
=4.
On taking cubes on both sides,
∴(x+
x
1
)
3
=4
3
∴x
3
+
x
3
1
+3.x.
x
1
(x+
x
1
)=64
∴x
3
+
x
3
1
=64−3.x.
x
1
(x+
x
1
)
∴x
3
+
x
3
1
=64−3(x+
x
1
)
=64−3(4)
=64−12=52.
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