Solution : Given that,
x a b
6 1 1
? 6 ab (ab)x[multiplying both the sides by abx]i.e.,
( )6
a bab
x
or,
a bb
ax
2
3b a bb a b
x ax a
?
22
33
[by componendo and dividendo]or,
b a
a b
x ax a
3
33Again,
a b
a
bx
2
3or,
a a b
a a b
x bx b
22
33
[by componendo and dividendo]?
a b
a b
x bx b
3
33Now,
a b
a b
b aa b
x bx b
x ax a
3 3
33
33b aa b
b aa b
3 3
b aa b a b
3 3
b ab a
2 ( )(^2).
2.
3
3
3
3
?
x b
x b
x a
x a
Example 7. If p
x x
x x
1 1
(^11) , prove that,^2 ^2 1 0.
x
p
p
Solution : Given that, p
x x
x x
1 1
1 1
1
1
1 1 1 1
1 1 1 1
?
p
p
x x x x
x x x x
[by componendo - dividendo]
1
1
1
1
1
1
21
21
or, or,
p
p
x
x
p
p
x
x
2 1
2 1
( 1 )
( 1 )
1
or,^1
2
2
2
2
p p
p p
p
p
x
x [squaring both sides]