Question

x = √3+1/√3-1 ,y=√3-1/√3+1, then find x²+y²+xy


plz answer​

Answer 1

Answer:

x² + y² + xy  = 15

Step-by-step explanation:

Given:- x = √3 + 1/√3 - 1 and y = √3 - 1/√3 + 1

Solution:

So, x + y

= (√3 + 1)/(√3 - 1) + (√3 - 1)/(√3 + 1)

= {(√3+1)(√3+1)+(√3-1)(√3-1)}/(√3-1)(√3+1)

= (3 + 2√3 + 1 + 3 - 2√3 + 1)/(3 - 1)

= 8/2

= 4

So, (x + y)²

= 4²

= 16

and, xy

= (√3 + 1)/(√3 - 1) × (√3 - 1)/(√3 + 1)

= (3 - 1)/(3 - 1)

= 2/2

= 1

∴ x² + y² + xy

= (x + y)² - 2xy + xy

= (x + y)² - xy

= 16 - 1

= 15