untitled

Example 5. Solve : 1 , 0 2 2.

1

1

1

1

b a b

bx

bx

ax

ax

  









Solution : Given that, 1

1

1

1

1









bx

bx

ax

ax

ax

ax

bx

bx









?

1

1

1

1

2

2

( 1 )

( 1 )

1

1

or,

ax

ax

bx

bx









[squaring both the sides]

2 2

2 2

1 2

1 2

1

1

or,

ax ax

ax ax

bx

bx

 

 





2 2 2 2

2 2 2 2

1 2 1 2

1 2 1 2

1 1

1 1

or,

ax ax ax ax

ax ax ax ax

bx bx

bx bx

    

    

  

  

[by componendo and dividendo]

ax

ax

bx 4

2 ( 1 )

2

2

or,

^22

ax

ax

bx 2

1 1

or,

^22

or, 2 ax bx( 1 a^2 x^2 )
or, x{ 2 ab( 1 a^2 x^2 )} 0
? itherE x 0 or 2 ab(aa^2 x^2 ) 0

1

2

or,

2

or,

or, ) 2

2 2

22

2 2

1

( 1







b

a

ax

b

a

ax

b ax a

1

1 2

1

1 2

or,^22

? r 

̧

¹

·

̈

©

§ 

b

a

a

x

b

a

a

x

? Required solution x 0 , 1
1 2
r 
b

a

a

x.

Example 6. If

x a b

6 1 1

 , show that 2 ,.

3

3

3

3

a b

x b

x b

x a

x a

z