Question

5. If x=
V3+1
V3 - 1
and y =
V3 - 1
3+1
O A 10
then the value of (x2 + y2) is:
OB. 13
O C. 14
D. 15​

Answer 1

Answer :

Given that,

x = (√3 + 1)/(√3 - 1)

and y = (√3 - 1)/(√3 + 1)

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