Question

Co x,y là hai số nguyên khác 0 nếu \(\dfrac{1}{x}+\dfrac{1}{y}=5\) và \(\dfrac{1}{x}-\dfrac{1}{y}=1\) thì tổng giá trị x + y

Answer 1

Ta có: \(\dfrac{1}{x}\) + \(\dfrac{1}{y}\)=5 \(\Rightarrow\) \(\dfrac{x+y}{xy}\)=5 \(\Rightarrow\) x+y = 5xy (1)

\(\dfrac{1}{x}\) - \(\dfrac{1}{y}\) =1 \(\Rightarrow\) \(\dfrac{y-x}{xy}\)=1 \(\Rightarrow\) y-x= xy (2)

Lấy (1)+(2), ta được: x+y+y-x=5xy+xy

\(\Leftrightarrow\) 2y = 6xy

\(\Leftrightarrow\) 2=6x

\(\Leftrightarrow\) x = \(\dfrac{1}{3}\)(3)

Ta có y-x=xy \(\Leftrightarrow\) y- xy=x \(\Leftrightarrow\) y- \(\dfrac{1}{3}\)y = \(\dfrac{1}{3}\)

\(\Leftrightarrow\) \(\dfrac{2}{3}\)y=\(\dfrac{1}{3}\)

\(\Leftrightarrow\) y = \(\dfrac{1}{2}\) (4)

Từ (3),(4) \(\Rightarrow\) x+y = \(\dfrac{1}{3}\)+ \(\dfrac{1}{2}\)=\(\dfrac{5}{6}\)

Vậy x +y = \(\dfrac{5}{6}\)

Đúng thì tick cho mình 1 cái nha

Answer 2

5/6

Answer 3

5/6 ak