if x-y=4 find which of the following sentence is correct a)x^3-y^3-12xy=64 b)x^3-y^3-3xy=64 c)x^3-y^3-12xy=12 d)x^3-y^3-4xy=64
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Answer:
We know that,
a
3
+b
3
+c
3
=(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)+3abc
If a+b+c=0, then a
3
+b
3
+c
3
=3abc
Now, given x
3
+y
3
−12xy+64 and
x+y=−4
=>x+y+4=0
Here, a=x, b=y, c=4 and a+b+c=x+y+4=0
Therefore
x
3
+y
3
+64=3xy(4)
=12xyz
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