The value of y when x + y/xy = 2, x - y/xy = 6 is…………………

1.	The value of y when x + y/xy = 2, x - y/xy = 6 is…………………A) 1/4B) -1/2C) -1/4D) 1/3
Answer» Correct option is (A) 1/4 \(\frac{x+y}{xy}=2\;and\;\frac{x-y}{xy}=6\) \(\Rightarrow\) \(\frac1x+\frac1y=2\) ________(1) and \(\frac1y-\frac1x=6\) ________(2) Put \(\frac1x=X\;\&\;\frac1y=Y,\) then equations (1) & (2) converts into X + Y = 2 ________(3) Y - X = 6 ________(4) Adding equations (3) & (4), we get (X + Y) + (Y - X) = 2+6 \(\Rightarrow\) 2Y = 8 \(\Rightarrow\) Y = \(\frac82\) = 4 \(\therefore\) X = 2 - Y = 2 - 4 = -2 \(\because\) X = -2 \(\Rightarrow\) \(\frac1x=-2\) \(\Rightarrow\) \(x=\frac{-1}2\) and Y = 4 \(\Rightarrow\) \(\frac1y=4\) \(\Rightarrow\) \(y=\frac14\) Correct option is A) 1/4

The value of y when x + y/xy = 2, x - y/xy = 6 is…………………A) 1/4B) -1/2C) -1/4D) 1/3

Answer»

Correct option is (A) 1/4

\(\frac{x+y}{xy}=2\;and\;\frac{x-y}{xy}=6\)

\(\Rightarrow\) \(\frac1x+\frac1y=2\) ________(1)

and \(\frac1y-\frac1x=6\) ________(2)

Put \(\frac1x=X\;\&\;\frac1y=Y,\) then equations (1) & (2) converts into

X + Y = 2 ________(3)

Y - X = 6 ________(4)

Adding equations (3) & (4), we get

(X + Y) + (Y - X) = 2+6

\(\Rightarrow\) 2Y = 8

\(\Rightarrow\) Y = \(\frac82\) = 4

\(\therefore\) X = 2 - Y

= 2 - 4 = -2

\(\because\) X = -2

\(\Rightarrow\) \(\frac1x=-2\)

\(\Rightarrow\) \(x=\frac{-1}2\)

and Y = 4

\(\Rightarrow\) \(\frac1y=4\)

\(\Rightarrow\) \(y=\frac14\)

Correct option is A) 1/4