1. Prove that given that a, b, and c are positive real numbers.
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2. Prove that given that x, y, and z are positive real numbers.
the questions you've been asking do not belong to "Advanced Algebra" forum. we have a forum for inequalities. anyway, here's a solution to your problems:
expanding gives us:
therefore but again by (1): thus:
now in (1) put and then divide by to prove your first problem and in (2) put and then divide by to prove your second problem.
On the first inequality, we can start by using
(try expanding the left hand side to see that this is true).
Thus
But if x,y, and z are all positive, then xyz is positive. And as is the sum of three squares, it cannot be negative. Thus . From our above equality, then, we have
--Kevin C.
Where is the forum for inequalities? I don't think these problems fit under the category of "Solving and Graphing Inequalities" for Elementary and Middle School Math Help (http://www.mathhelpforum.com/math-help/inequalities/).
Also, I don't understand your solution. Could you please indicate which parts correspond to which question? Thanks!