Question

If x=
√5-√2 /√5 + √2
and y =
√5 + √2 /√5 - √2
find the value of x^2 + xy + y^2​

Answer 1

Given, x = ( √5 – 2 ) / ( √5 + 2 ) and y = ( √5 + 2 ) / ( √5 – 2 )

x = ( √5 – 2 ) / ( √5 + 2 )

= ( √5 – 2 ) / ( √5 + 2 ) × ( √5 – 2 ) / ( √5 – 2 )

= ( √5 – 2 )² / [ (√5)² – (2)² ]

= ( 9– 4√5 ) / ( 5 – 4 )

= 9 – 4 √5

y = ( √5 + 2 ) / ( √5 – 2 )

= ( √5 + 2 ) / ( √5 – 2 ) × ( √5 + 2 ) / ( √5 + 2 )

= ( √5 + 2 )² / [ (√5)² – (2)² ]

= ( 9 + 4√5 ) / ( 5 – 4 )

= 9 + 4√5

Now, x² + xy + y²

= ( 9 – 4√5 )² + ( 9 – 4√5)( 9 + 4√5 ) + ( 9 + 4√5 )²

= ( 81 – 72√5 + 80 ) + [ 9( 9 + 4√5 ) –4√5( 9 + 4√5 ) ] + ( 81 + 72√5 + 80 )

= ( 161 – 72√5 ) + ( 81 + 13√5 – 13√5 – 80 ) + ( 161 + 72√5 )

= 161 – 72√5 + 1 + 161 + 72√5

= 161 + 1 + 161

= 323

Answer 2

Answer:

18.7

Step-by-step explanation:

By doing directly

x = 7-2√10 /3

y = 7+2√10 /3

x²+xy+y² = (x+y)²-xy  =14²/3² - 3

             = 18.7

PLEASE MARK THIS ANSWER AS THE BRAINLIEST ANSWER