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Kissing
Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
Good Approximations
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
Target Six
Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
Age 16 to 18
Challenge Level
Make a substitution to find two exact real solutions to the equation $(x + 3)^4 + (x + 5) ^4 = 20.$
Did you know ... ?
Frequently mathematicians spend their time stuck wondering how to solve equations or problems. One way of cracking a tough problem is to make a transformation to turn it into a more familiar form which allows the solution to proceed. Finding good substitutions or transformations is one of the more creative aspects of mathematics.
Frequently mathematicians spend their time stuck wondering how to solve equations or problems. One way of cracking a tough problem is to make a transformation to turn it into a more familiar form which allows the solution to proceed. Finding good substitutions or transformations is one of the more creative aspects of mathematics.
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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.