Question

If x = √5 - √2 / √5 + √2 AND y = √5 + √2 / √5 - √2 , find the value of x² + y² + xy​

Answer 1

Answer:

x² + y² + xy​ = 20.78

Step-by-step explanation:

x = (√5 - √2) / (√5 + √2)

y = (√5 + √2) / (√5 - √2)

x² + y² + xy​

= ( x + y ) ² - xy

x + y = (√5 - √2) / (√5 + √2)  +  (√5 + √2) / (√5 - √2)

=>x + y =( (√5 - √2)² +  (√5 + √2)²) / (√5² - √2²)

=>x + y =(5 + 2 - 2√5 √2 + 5 + 2 + 2√5 √2) / (5 - 2)

=>x + y =(14) / (3)

=> x +y = 14/3

xy =( (√5 - √2) / (√5 + √2) ) ×( (√5 + √2) / (√5 - √2))

xy = 1

( x + y ) ² - xy

= (14/3)² - 1

= 196/9 - 1

= (196-9)/9

= 187/9

= 20.78