Question

If x=√5-√2/√5+√2 and y=√5+√2/√5-√2 then find the value of x²+xy+y2. will mark as brainliest​

Answer 1

Step-by-step explanation:

x²+xy+y²={(√5-√2÷√5+√2)+(√5+√2÷√5-√2)}²

x²+xy+y²={(√5-√2)(√5-√2)+(√5+√2)(√5+√2)÷(√5+√2)(√5-√2)}²

x²+xy+y²={(√5-√2)²+(√5+√2)²÷(√5)²-(√2)²}²

x²+xy+y²=[{(√5)²-(√2)²}²÷5-3]²

x²+xy+y²={(5-2)²÷3}²

x²+xy+y²={(3)²÷3}²

x²+xy+y²={9÷3}²

x²+xy+y²=(3)²

x²+xy+y²=9

Answer 2

Hey there !!

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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