Question

ChoN=\(\dfrac{7-x}{5-x}\)

a,tìm x thuộc Z để N có giá trị nguyên

b,tìm x thuộc Z để N có giá trị lớn nhất

Answer 1

a,

\(N\in Z\Leftrightarrow7-x⋮5-x\)

\(\Leftrightarrow\left(5-x\right)+2⋮5-x\)

\(\Leftrightarrow2⋮5-x\)

\(\Rightarrow5-x\inƯ\left(2\right)\in\left\{-2;-1;1;2\right\}\)

\(\Rightarrow x\in\left\{3;4;6;7\right\}\)

b,

\(N\cdot x=\dfrac{7x-x^2}{5-x}=\dfrac{-\left(x^2-7x+\dfrac{49}{4}\right)+\dfrac{49}{4}}{5-x}=\dfrac{-\left(x-\dfrac{7}{2}\right)^2}{5-x}+\dfrac{\dfrac{49}{4}}{5-x}\ge\dfrac{\dfrac{49}{4}}{5-x}\)

Dấu "=" khi \(x=\dfrac{7}{2}\Leftrightarrow N=\dfrac{\dfrac{\dfrac{49}{4}}{5-x}}{x}=\dfrac{7}{3}\)