Câu hỏi của TNT GAMING

Question

1,tìm x biết:$\left|2x+3\right|+\left|2x-1\right|=\dfrac{8}{3.\left(x+1\right)^2+2}$

Nguyễn Việt Lâm · Accepted Answer

Lại có: $3\left(x+1\right)^2+2\ge2\Rightarrow\dfrac{8}{3\left(x+1\right)^2+2}\le\dfrac{8}{2}=4$

$\Rightarrow VP\le4\Rightarrow VT\ge VP$

Dấu "=" xảy ra khi:

$\left\{{}\begin{matrix}\left(2x+3\right)\left(1-2x\right)\ge0\3\left(x+1\right)^2+2=2\end{matrix}\right.$ $\Rightarrow x=-1$

Lại có: $3\left(x+1\right)^2+2\ge2\Rightarrow\dfrac{8}{3\left(x+1\right)^2+2}\le\dfrac{8}{2}=4$

$\Rightarrow VP\le4\Rightarrow VT\ge VP$

Dấu "=" xảy ra khi:

$\left\{{}\begin{matrix}\left(2x+3\right)\left(1-2x\right)\ge0\3\left(x+1\right)^2+2=2\end{matrix}\right.$ $\Rightarrow x=-1$

Vậy pt có nghiệm duy nhất $x=-1$

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