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Question
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
Options
1
–1
0
`1/2`
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Solution
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is 0.
Explanation:
Consider the equation:
`x/y + y/x = -1`
Simplify the above expression as follows:
`(x^2 + y^2)/(xy) = -1`
x2 + y2 = –xy
Now, x3 – y3 = (x – y)(x2 + y2 + xy)
= (x – y)(–xy + xy) ...[Substitute: x2 + y2 = –xy]
= (x – y) × 0
= 0
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