Question
Download Solution PDFIf x - y = 1, then what is the value of x3 - y3 - 3xy?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
If x - y = 1
Formula used:
x3 - y3 - 3xy = (x - y)(x2 + xy + y2) - 3xy
Calculation:
x - y = 1
⇒ x3 - y3 - 3xy = 1(x2 + xy + y2) - 3xy
⇒ x3 - y3 - 3xy = x2 + xy + y2 - 3xy
⇒ x3 - y3 - 3xy = x2 + y2 - 2xy
⇒ x3 - y3 - 3xy = (x - y)2
⇒ x3 - y3 - 3xy = 12
⇒ x3 - y3 - 3xy = 1
∴ The correct answer is option (2).
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