11) \(\frac{α}{β}> \frac{2α-β}{α+4β} \) multiply by α+4β and β and its >0 because α,β its positive numbers
\(α(α+4β)>β(2α-β) <=> α^2+4αβ > 2αβ-β^2 <=> α^2 +4αβ - 2αβ + β^2 >0 <=> α^2 +2αβ + β^2 >0 <=> (α+β)^2>0 \)
where applicable! So we prove it!
12) Something is wrong here or I don't understand the question:
exp.:\(3^2-2^2=9-4=5\) But there is no sum of two consecutive odd numbers be equal with 5 because 1+3 = 4 and general sum of two consecutive odd numbers is allways be equal with even number because if n is a number we have:
n+(n+2)=2n+2 = 2(n+1) for every n natural so we have 2(n+1)
is divided by 2 so it's even number and 5(in this example) it's not even number.
Hope this helps!
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