**** MathMagic Problem Cycle 7 (rec): Level 10-12 Regular *****
A diophantine equation is an equation in which only integer
solutions are desired. Example: a solution to 3x + 4y = 11 is
x= 1 and y = 2 since 3(1) + 4(2) = 11
1) Find TWO sets of solutions to the diophantine equations and
explain your solution strategy.
a) 5x + 4y = 32 b) 6x + 4y = 18
2) A school ordered books and calculators. The books cost $8
each and the calculators cost $10 each.
a) Write an equation which can be used to represent the cost
of the books and calculators is $74 was spent.
b) How many books and how many calculators could the school
have purchased?
----------------------------------------------------------------------
***** MathMagic Problem Cycle 7 (rec): Level 10-12 Advanced *****
Radical Numbers
---------------
1) Solve for x: x^2 + x - 1 = 0. (x^2 means x to the power of 2)
The positive result is called the Golden Mean. What is the value
of the reciprocal of this number? Compare the numbers in decimal
form using a calculator. What do you notice?
2) What is the value of \| (2 + \| (2 + \| (2 +... )))
where \| means square root and they are nested, one square root
inside the other?
How about the value of \| (6 + \| (6 + \| (6 + ... ))) ?
----------------------------------------------------------------------