If x
3
−y
3
=40 and x−y=4, then find the value of xy.
- A60
- B-2
- C-60
- D2
Solution & Step-by-step Explanation
We can use the standard algebraic identity for the difference of two cubes:
x
3
−y
3
=(x−y)(x
2
+xy+y
2
)
Alternatively, we can express it in terms of (x−y) and xy:
x
3
−y
3
=(x−y)
3
+3xy(x−y)
Substitute the given values into the equation:
40=(4)
3
+3xy(4)
40=64+12xy
12xy=40−64
12xy=−24
$$
xy = \frac{-24}{12} = -2
x
3
−y
3
=(x−y)(x
2
+xy+y
2
)
Alternatively, we can express it in terms of (x−y) and xy:
x
3
−y
3
=(x−y)
3
+3xy(x−y)
Substitute the given values into the equation:
40=(4)
3
+3xy(4)
40=64+12xy
12xy=40−64
12xy=−24
$$
xy = \frac{-24}{12} = -2