1) with out actual calculating the cabes, find the value of each of the following (i) [1/2)3+(1/3)3-(5/6)3
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Answer:
Let
a=
2
1
,b=
3
1
,c=−
6
5
Here
a+b+c=
2
1
+
3
1
−
6
5
=
6
3+2−5
=
6
0
=0
We know that
a
3
+b
3
+c
3
=3abc when a+b+c=0
∴(
2
1
)
3
+(
3
1
)
3
−(
6
5
)
3
=(
2
1
)
3
+(
3
1
)
3
+(−
6
5
)
3
=3×
2
1
×
3
1
(−
6
5
)
=−
12
5
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