Difference between revisions of "MIE 2016/Problem 9"
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− | Substituting all the known values, we get <math>x^3+y^3+z^3= | + | Substituting all the known values, we get <math>x^3+y^3+z^3=343-3((7)(12)-48) = 235</math>. <math>\boxed{\textbf{b}}</math>. |
Latest revision as of 15:14, 8 January 2018
Problem 9
Let ,
and
be complex numbers that satisfies the following system:
Compute .
(a)
(b)
(c)
(d)
(e)
Solution 1
We start by expanding .
As we are given and
, we get
is
.
Next, we simplify the third case and obtain
As we know is
, we know
is
Next we expand
Rearranging the equation we arrive at
Substituting all the known values, we get .
.