(VIII ) 1 / (3X + Y ) + 1 / (3X - Y ) = 3 / 4 -------->(1)
1 / 2 (3X + Y ) - 1 / 2 (3X - Y ) = -1 / 8
=> 1 / (3X + Y ) - 1 / (3X - Y ) = - 1 / 4 -------> (2)
मान लीजिये 1 / (3X + Y) = S एवं 1 / (3X - Y) = t
=> s + t = 3 / 4 -----> (3 )
=> s - t = -1 / 4 -----> (4)
समीकरण (3 ) व समीकरण (4 ) जोड़ने पर ,
2s = 1 / 2
s = 1 / 4
1 / (3x +y) = 1 / 4
3x + y = 4 -------> (5 )
समीकरण (3 ) व (4 ) से घटाने पर ,
2t = 1
t = 1 / 2
1 / (3x - y ) = 1 / 2
3x - y = 2 --------> (6 )
समीकरण (5 ) व (6 ) को जोड़ने पर ,
6x = 6 => x = 6 / 6 = 1
x = 1
समीकरण ( 5 ) में से (6 ) घटाने पर ,
2 y = 2
y = 2 / 2
y = 1
उत्तर : x = 1 और y = 1
(VIII) 1 / (3X + Y ) + 1 / (3X - Y ) = 3 / 4 -------->(1)
1/2 (3X + Y ) - 1/2 (3X - Y ) = -1 / 8
=> 1 / (3X + Y ) - 1 / (3X - Y ) = - 1 / 4 -------> (2)
Let 1 / (3X + Y) = S and 1 / (3X - Y) = t
=> s + t = 3/4 -----> (3 )
=> s - t = -1/4 -----> (4)
Adding equation (3) and equation (4),
2s = 1/2
s = 1/4
1 / (3x +y) = 1/4
3x + y = 4 -------> (5)
Subtracting from equation (3) and (4),
2t = 1
t = 1/2
1 / (3x - y ) = 1/2
3x - y = 2 --------> ( 6 )
Adding equations (5) and (6) we get
6x = 6 => x = 6 / 6 = 1
x = 1
Subtracting (6) from equation ( 5 ) ,
2 y = 2
y = 2 / 2
y = 1
Answer: x = 1 and y = 1