Ta có: x−y1=x+y7=(x−y)+(x+y)1+7=2x8=x4x−y1=x+y7=(x−y)+(x+y)1+7=2x8=x4

xy=xy24⇔6x24=xy24xy=xy24⇔6x24=xy24

⇒6x=xy⇒6x=xy

⇒y=6⇒y=6

x−61=x+67x−61=x+67

⇔7.(x−6)=x+6⇔7.(x−6)=x+6

⇔7x−42=x+6⇔7x−42=x+6

⇔7x−x=6+42⇔7x−x=6+42

⇔6x=48⇔6x=48

⇒x=8⇒x=8

Vậy x=8;y=6

Ta có : \(\frac{x-y}{1}=\frac{x+y}{7}=\frac{\left(x-y\right)+\left(x+y\right)}{1+7}=\frac{2x}{8}=\frac{x}{4}\)

\(\frac{x}{4}=\frac{xy}{24}\Leftrightarrow\frac{6x}{24}=\frac{xy}{24}\) => 6x = xy => y = 6

\(\frac{x-6}{1}=\frac{x+6}{7}\)

<=> 7(x - 6) = x + 6

<=> 7x - 42 = x + 6

<=> 7x - x = 6 + 42

<=> 6x = 48

=> x = 8

Vậy x = 8 ; y = 6

cho hai số x,y thỏa mãn x+y=x.y=x/y, với y khác 0. Tính giá trị biểu thức P=2022x+2021y - Hoc24

\(ĐK:y\ne0\)

\(x+y=\dfrac{x}{y}\Leftrightarrow xy+y^2=x\)

Mà \(xy=x+y\Leftrightarrow x+y+y^2=x\)

\(\Leftrightarrow y\left(y+1\right)=0\Leftrightarrow y=-1\left(y\ne0\right)\\ \Leftrightarrow x-1=\dfrac{x}{-1}=-x\\ \Leftrightarrow2x-1=0\Leftrightarrow x=\dfrac{1}{2}\)

Vậy \(P=2022\cdot\dfrac{1}{2}+2021\left(-1\right)=1011-2021=-1010\)