Friday, May 4, 2012

A Classic Algebra Challenge

Once students learn the strategy for doing these kinds of questions, the SAT and other standardized tests seem rather easy!

x+y=10
x^2+y^2=10
Find x^3+y^3

Ans: -350

Notes: 

(1) Before giving students this question you may wish to scaffold with finding xy first.
Ans: 45

(2)  To promote connection-making and to deepen their thought processes, give them the answer -350 and ask:
(a)  Without graphing. explain why the graphs of the 2 given eqns DO NOT INTERSECT!
(b) Then how can there be a solution!

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