Question

If 1 / X - 1 / Y is equals to 6 / 7 and x y is equals to 7 then x, y are

Answer 1

1 1 6
--- + ---- = ------
X Y 7

X + Y 6
--------- = ----
XY 7

X + Y 6
--------- = ---- [ XY= 7 given ]
7 7

X+Y = 7*6/7

X + Y = 6 ....................i)

We know (X-Y)² = (X+Y)² - 4XY

putting the value of (X+Y) and XY, we get

(X-Y)² = 6² - 4*7 = 36 - 28 = 8

or X - Y = √8 = √4*2 = 2√2 .....................ii)

Adding i) and ii),

2X = 6+2√2 = 2(3+√2)

or X = 2(3+√2)/2 = (3+√2)

Now from i)

Y = 6 - X = 6 - (3+√2) = (3-√2)

Hence X= 3+√2, Y = 3-√2 Ans.