Question

[Quang Đẹp Trai]

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

Answer 1

[Nguyễn thành Đạt]

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

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

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

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

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

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

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