Question

plz give me solution fast

Answer 1

               1
= -----------------------------
     √6 + √5 - √11

By multiplying the numerator and denominator by { ( √6 + √5 ) + √11 }.

= 1 { ( √6 + √5 ) + √11 } / { ( √6 + √5 ) - √11 } { ( √6 + √5 ) + √11 }.




= { ( √6 + √5 ) + √11 } / { ( √6 + √5 )^2 - ( √11 )^2 }


= { ( √6 + √5 ) + √11 } / { 6 + 5 + 2√30 - 11 }


= { ( √6 + √5 ) + √11 } / { 11 - 11 + 2√30 }

= { ( √6 + √5 ) + √11 } / ( 2√30 )


      { ( √6 + √5 ) + √11 }
=  -------------------------------------
                    2√30

Now by multiplying numerator and denominator by √30 .


=  ( √6 + √5 + √11 ) √30 / ( 2√30 ) ( √30 )


     6√5 + 5√6 + √330
= -------------------------------------
                 60

Answer 2

Solution for question 4.

Given , x = 9 + 4√5.

So, 1/x = 1 / ( 9 + 4√5 ).

By multiplying numerator and denominator by ( 9 - 4√5 ).

= 1 ( 9 - 4√5 ) / ( 9 + 4√5 ) ( 9 - 4√5 )

= ( 9 - 4√5 ) / { ( 9 )^2 - ( 4√5 )^2 } [ ( a + b ) ( a - b ) = a^2 - b^2 ]

= ( 9 - 4√5 ) / { 81 - 80 }

= ( 9 - 4√5 ).

Now .

= √x + 1/√x

By substituting the value of x and 1/x.

= √( 9 + 4√5 ) + √( 9 - 4√5 )

By squaring and then rooting it.

= √[{ √( 9 + 4√5 ) + √( 9 - 4√5 ) }^2 ]

= √[ { 9 + 4√5 + 9 - 4√5 + 2 ( 9 + 4√5 ) ( 9 - 4√5 ) ]

= √ [ 18 + 2 { ( 9 )^2 - ( 4√5 )^2 } ]

= √ [ 18 + 2 { 81 - 80 } ]

= √ [ 18 + 2 ]

= √20

= 2√5.