Toán đại lớp 10

N

noinhobinhyen

$\Leftrightarrow 5\sqrt{5x^2+10x+9} = 5m+35-10x-5x^2$

$\Leftrightarrow 5\sqrt{5x^2+10x+9} = -(5x^2+10x+9)+44+5m$

$\Leftrightarrow (5x^2+10x+9) + 5\sqrt{5x^2+10x+9}-5m-44=0 (1)$

Đặt $t=\sqrt{5x^2+10x+9}$

$\forall x \geq 3 \Rightarrow t \in [2\sqrt{21};+\infty)$

$pt(1) : t^2+5t-44=5m$

Xét $f(t) = t^2+5t-44 \forall t \in [2\sqrt{21};+\infty)$

$\Rightarrow f(t) \in [40+10\sqrt{21};+\infty)$

$\Rightarrow 5m \in [40+10\sqrt{21};+\infty)$

$\Leftrightarrow m \in [8+2\sqrt{21};+\infty)$
 
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