Example 16. If a^2  3 a 1 0 , what is the value of^33
1
a

a ?

Solution : Given that, a^2  3 a 1 0

or,a^2  1 3 a or, 3

(^21)

a
a
or, 3
(^21)

a a
a
or, 3
1

a
a
? Given expression =^33
1
a
a 
= ̧
¹
·
̈
©
 ˜ § 
̧
¹
·
̈
©
§ 
a
a
a
a
a
a
1 1
3
1
3

= 3 ]

1

3 3 3 [

3

 

a

a

= 3 3  3 3
= 0
Example 17. Simplify :

(ab)(a^2 abb^2 )(bc)(b^2 bcc^2 )(ca)(c^2 caa^2 )

Solution :(ab)(a^2 abb^2 )(bc)(b^2 bcc^2 )(ca)(c^2 caa^2 )

=a^3 b^3 b^3 c^3 c^3 a^3

= 0

Example 18. If a 3  2 , prove that, 18 3.

1

3

(^3) 
a
a
Solution : Given that, a 3  2
?
3 2
1 1

a

3 23 2

3 2

 

 [multiplying numerator and denominator by 3  2 ]

=

2 2

3 2

3 2



 =

3 2

3 2





= 3  2

? 3 2 3 2

1

   

a

a

= 3  2  3  2 2 3