|December 6th, 2016, 01:43 PM||#1|
Joined: Dec 2016
Condition of inequation
I have two sets of numbers satisfying:
Whether it is the case:
x1^2+x2^2+...+xn^2>=y1^2+y2^2+...+yn^2 (xi^2 presents the square of xi).
xi,yi here are not negative numbers.
|December 6th, 2016, 03:40 PM||#2|
Joined: May 2007
Proof by mathematical induction. Assuming you want to prove it for all n.
x1>y1 implies x1^2>y1^2
x2>y2 implies x2^2>y2^2
Add together and get x1+x2>y1+y2 implies x1^2+x2^2>y1^2+y2^2
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