the mean of x,1\x is m,then find the mean of x3,1\x3
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Answer:
Given mean x and
x
1
is M
∴M=
2
x+
x
1
⇒x+
x
1
=2M
Cube both the sides
∴(x+
x
1
)
3
=(2M)
3
⇒x
3
+
x
3
1
+3(x+
x
1
)=8M
3
⇒x
3
+
x
3
1
=8M
3
−3(x+
x
1
)
⇒x
3
+
x
3
1
=8M
3
−3(2M)
⇒x
3
+
x
3
1
=2M(4M
2
−3)
Then mean of x
3
and
x
3
1
So
2
x
3
+
x
3
1
=2M(4M
2
−3)⇒x
3
+
x
3
1
=M(4M
2
−3)
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