13 tháng 3 2022 lúc 8:44
3s hàm đặc trưng :v
\(pt\Leftrightarrow\left[h\left(x\right)-2\right]^3+3\left[h\left(x\right)-2\right]=\left(x+2\right)\sqrt{x-1}\)
\(\Leftrightarrow\left(h\left(x\right)-2\right)\left[\left(h\left(x\right)-2\right)^2+3\right]=\sqrt{x-1}\left(x+2\right)\)
\(f\left(t\right)=t\left(t^2+3\right)=t^3+3t\Rightarrow f'\left(t\right)=3t^2+3>0\forall t\) => don dieu
\(\Rightarrow h\left(x\right)-2=\sqrt{x-1}\Rightarrow P=x-4\left(\sqrt{x-1}+2\right)=x-4\sqrt{x-1}-8\)
\(\sqrt{x-1}=t\Rightarrow x=t^2+1\Rightarrow P=t^2-4t-7\forall x\in[1;+\infty)\)
Bấm máy ra P=-11 :v
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