- #1
halo31
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simple proof help??
The question states: Let rεQ+ Prove that if (r^2+1)/(r)≤1, then (r^2+2)/(r)≤2.
I wanted to prove it trivially by proving it is true for all Q(x). would this be a correct way?
Since (r^2+2)/(r)≤2= (r-1)^2+1≤ 0 it follows (r-1)^2≤-1 for all rεQ+. Therefore (r^2+2)/(r)≤2.
Homework Statement
The question states: Let rεQ+ Prove that if (r^2+1)/(r)≤1, then (r^2+2)/(r)≤2.
I wanted to prove it trivially by proving it is true for all Q(x). would this be a correct way?
Homework Equations
The Attempt at a Solution
Since (r^2+2)/(r)≤2= (r-1)^2+1≤ 0 it follows (r-1)^2≤-1 for all rεQ+. Therefore (r^2+2)/(r)≤2.