2006 iTest Problems/Problem 35
Problem 35
Compute the of ordered quadruples of complex numbers (not necessarily nonreal) such that the following system is satisfied:
Solution
as we are given , so from this we get second equation as . so say . so we get . from fourth equation we get . so we get . also from third equation we get . notice we want and . so . so this gives . and . so we get a equation whose roots are . so we get . this gives . and three distinct complex ( not necessarily non real) solutions. so as 1. we get any one pair say . so for some . so as , will be distinct we will get quadruples from solution so we can have such quadruples.
~https://artofproblemsolving.com/community/q1h1745445p11362157
See also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem 34 |
Followed by: Problem 36 | |
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