Question

If (x - y) = 6 and xy = 1, then the value of
x^3 - y^3 is
(a) 324
(b) 432 (c) 234
(d) 322​

Answer 1

Answer:

c) 234

$(x - y) {}^{3} = {x}^{3} - y {}^{3} - 3xy(x - y) \\ (6) {}^{3} = x {}^{3} - y {}^{3} - 3(1)(6) \\ (it \: is \: given \: that \: xy \: = 1 \: and \: (x - y) = 6) \\ 216 = {x}^{3} - y {}^{3} - 18 \\ 216 + 18 = x {}^{3} - y {}^{3} \\ 234 = x {}^{3 } - y {}^{3}$

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