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.