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Question

A = x - x ^ 2 - 1 <0. với mọi x

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HT.Phong (9A5) · Accepted Answer

$A=x-x^2-1$

$A=-\left(x^2-x+1\right)$

$A=-\left(x^2-2\cdot\dfrac{1}{2}x+\dfrac{1}{4}+\dfrac{3}{4}\right)$

$A=-\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{4}$

Mà: $-\left(x-\dfrac{1}{2}\right)^2\le0\forall x$

Và: $-\dfrac{3}{4}< 0$

$\Rightarrow A=-\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{4}< 0\forall x$Câu trả lời: $A=x-x^2-1$

$A=-\left(x^2-x+1\right)$

$A=-\left(x^2-2\cdot\dfrac{1}{2}x+\dfrac{1}{4}+\dfrac{3}{4}\right)$

$A=-\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{4}$

Mà: $-\left(x-\dfrac{1}{2}\right)^2\le0\forall x$

Và: $-\dfrac{3}{4}< 0$

$\Rightarrow A=-\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{4}< 0\forall x$