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Target Six
Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
8 Methods for Three by One
This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?
An Introduction to Complex Numbers
A short introduction to complex numbers written primarily for students aged 14 to 19.
Age 16 to 18 Challenge Level:
If \[z_1 z_2 z_3 = 1\] and \[z_1 + z_2 + z_3 = \frac{1}{z_1} + \frac{1}{z_2} +\frac{1}{z_3}\] then show that at least one of these numbers must be 1.
Now for the complexity! When are the other numbers real and when are they complex?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.