If x3 - y3 = 40 and x - y = 4, then find the value of xy.
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Correct answer: B
Explanation
The correct answer is option 2 i.e. -2.
x3 − y3 = (x − y)(x2 + xy + y2)
⇒ 40 = 4(x2 + xy + y2) ⇒ x2 + xy + y2 = 40/4 = 10 (1)
(x − y)2 = x2 + y2 − 2xy ⇒ 42 = x2 + y2 − 2xy ⇒ 16 = x2 + y2 − 2xy
From (1): x2 + y2 + xy = 10 ⇒ x2 + y2 = 10 − xy
16 = (10 − xy) − 2xy ⇒ 16 = 10 − 3xy ⇒ 3xy = 10 − 16 = −6 ⇒ xy = 3 − 6 = −2