Question

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

A) 1/4

B) -1/2

C) -1/4

D) 1/3

Answer 1

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

\(\Rightarrow\) \(\frac1y=4\)

\(\Rightarrow\) \(y=\frac14\)

Answer 2

Correct option is A) 1/4