Problem
ALG-B2-M08-P013 Product of triangle differences
#13
★★★★☆ Level 4 of 5
If \(a,b,c\) are triangle sides, prove \((b+c-a)(c+a-b)(a+b-c)>0\).
Hint. Use \(x=(b+c-a)/2\), \(y=(c+a-b)/2\), \(z=(a+b-c)/2\).
For triangle sides, \(x,y,z>0\). The product equals \(8xyz>0\).
Teaching goal: recognize the appropriate substitution and check the domain.