May 4, 2017

Inner Inequality


Edited: Jun 25, 2017

Suppose that we are told that four numbers a,b,c,d lie between -5 and 5. Suppose also that the numbers are constrained so that

5 < a+b < 10 and -10 < c+d < -5

Given this information, what can you deduce about these inequalities?

?? < a+b-c-d < ??

?? < a-c < ??

?? < a-c+d-b < ??

?? < abcd < ??


Did you know ... ?

There are many useful general inequalities in mathematics, such as the AM-GM, Cauchy-Schwarz and Jensen's inequalities. These general inequalities are powerful tools which greatly simplify a wide variety of problems in mathematics, in applications from integration to probability via linear algebra.

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