\(cos\left(2-ab\right)-cos\left(a+b\right)=a+b+ab-2\)
\(\Leftrightarrow cos\left(2-ab\right)+2-ab=cos\left(a+b\right)+a+b\)
Xét hàm \(f\left(x\right)=cosx+x\)
\(f'\left(x\right)=-sinx+1\ge0;\forall x\Rightarrow f\left(x\right)\) đồng biến trên R
\(\Rightarrow2-ab=a+b\)
\(\Rightarrow2-a=b\left(a+1\right)\Rightarrow b=\dfrac{2-a}{a+1}=\dfrac{3}{a+1}-1\)
\(\Rightarrow P=a+\dfrac{6}{a+1}-2=a+1+\dfrac{6}{a+1}-3\ge2\sqrt{\dfrac{6\left(a+1\right)}{a+1}}-3=2\sqrt{6}-3\)
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