Question

if x=5+2root6 and xy=1, find the value of x²+y²/xy​

Answer 1

Answer:

98

Step-by-step explanation:

Please find the attachment

Answer 2

Answer:

98

Step-by-step explanation:

⇒ x = 5 + 2√6

           Given,

                      xy = 1       ⇒ y = 1 / x

⇒ y = 1 / x

⇒ y = 1 / ( 5 + 2√6 )

Multiplying as well as dividing RHS by  5 - 2√6:

⇒ y = ( 5 - 2√6 ) / ( 5 + 2√6 )( 5 - 2√6 )

⇒ y = ( 5 - 2√6 ) / { 5^2 - ( 2√6 )^2 }             Using ( a + b )( a - b ) = a^2 - b^2

⇒ y = ( 5 - 2√6 ) / ( 25 - 24 )

⇒ y = ( 5 - 2√6 ) / 1

⇒ y = 5 -2√6

        Therefore,

⇒ x^2 + y^2

⇒ ( 5 + 2√6 )^2 + ( 5 - 2√6  )^2

⇒ { ( 5 )^2 + ( 2√6 )^2 + 2( 5 )( 2√6 ) } + { ( 5 )^2 + ( 2√6 )^2 - 2( 5 )( 2√6 ) }

⇒ 5^2 + ( 2√6 )^2 + 5^2 + ( 2√6 )^2

⇒ 25 + 24 + 25 + 24

⇒ 50 + 48

⇒ 98

Hope this helps!