Câu hỏi của Quang Đẹp Trai

Question

tìm gtnn và gtln của biểu thức:
P=$\dfrac{5x-9}{x-3}$

Nguyễn thành Đạt · Accepted Answer

Ta có : $P\text{=}\dfrac{5x-9}{x-3}\text{=}\dfrac{5x-15+6}{x-3}$

$\Rightarrow P\text{=}\dfrac{5x-15}{x-3}+\dfrac{6}{x-3}$

$\Rightarrow P\text{=}\dfrac{5\left(x-3\right)}{x-3}+\dfrac{6}{x-3}\text{=}\dfrac{6}{x-3}+5$

$\Rightarrow P_{max}\Leftrightarrow x-3\text{=}1\Leftrightarrow x\text{=}4$

$\Rightarrow P_{max}\text{=}9\Leftrightarrow x\text{=}4$

$\Rightarrow P_{min}\Leftrightarrow x-3\text{=}-1\Leftrightarrow x\text{=}2$

$\Rightarrow P_{min}\text{=}-1\Leftrightarrow x\text{=}2$Câu trả lời: Ta có : $P\text{=}\dfrac{5x-9}{x-3}\text{=}\dfrac{5x-15+6}{x-3}$

$\Rightarrow P\text{=}\dfrac{5x-15}{x-3}+\dfrac{6}{x-3}$

$\Rightarrow P\text{=}\dfrac{5\left(x-3\right)}{x-3}+\dfrac{6}{x-3}\text{=}\dfrac{6}{x-3}+5$

$\Rightarrow P_{max}\Leftrightarrow x-3\text{=}1\Leftrightarrow x\text{=}4$

$\Rightarrow P_{max}\text{=}9\Leftrightarrow x\text{=}4$

$\Rightarrow P_{min}\Leftrightarrow x-3\text{=}-1\Leftrightarrow x\text{=}2$

$\Rightarrow P_{min}\text{=}-1\Leftrightarrow x\text{=}2$