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Archimedes and Numerical Roots
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
Root to Poly
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
Age 14 to 16 Challenge Level:
Find integer solutions to: $${{\sqrt{a + b\sqrt{x}}} + {\sqrt{c + d\sqrt{x}}}} ={ 1}$$
Hint: As everything on the left is positive and the total is 1, there are only a few cases to consider.
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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.