if x-1/x=7 find x³-1/x3
Answers
Answered by
3
It is given that x+
x
1
=7, by taking cubes on both sides we get:
(x+
x
1
)
3
=7
3
⇒(x)
3
+(
x
1
)
3
+(3×x×
x
1
)(x+
x
1
)=343(∵(a+b)
3
=a
3
+b
3
+3ab(a+b))
⇒x
3
+
x
3
1
+3(7)=343(Givenx+
x
1
=7)
⇒x
3
+
x
3
1
+(3×7)=343
⇒x
3
+
x
3
1
+21=343
⇒x
3
+
x
3
1
=343−21
⇒x
3
+
x
3
1
=322
Hence, x
3
+
x
3
1
=322.
Answered by
0
Answer:
322
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