Question

if x-y=2and xy=24, find 1/x+ 1/y

Answer 1

Given,
x-y = 2 .
xy = 24 .

We know that,
( x - y) ² = (x+y)²-4xy
2² = (x+y)²-4(24)
4 + 96 = (x+y)²
( x + y) = √100 = 10 .

Now,
1/x + 1/y
= x + y / xy
= 10/24
= 5/12

Answer 2

x - y = 2
x = 2 +y ........ (1)
on putting this in xy = 24, we get
(2+y ) × y = 24
2y + y^2 = 24
y^2 + 2y - 24 =0
y^2 + 6y - 4y -24 =0 by factorisation
y (y+6) -4 (y+6) = 0
(y-4)(y+6) = 0
y = 4 or -6
on putting y =4 in (1)
x = 2+4 = 6
now
1/x + 1/y = x+y/xy = 4+6/24 = 10/24
Ans. 5/12