Question

help me my answers are not coming correct ...

Answer 1

x = (root 3 + 1)/(root3 - 1)
On rationalising the denominator, we get
x= 3+1+2root3 / 2
x= 2 + root3

Similarly,
y= 2 - root3

Now,
x^2 +xy - y^2
= (2+root3)^2 + (2+root3) (2- root3) - (2- root3)^2
= 4+3+4root3 + 4 - 3 - (4+3 - 4root3)
= 7 + 4root3 +1 - 7 + 4root3
= 1 + 8 root3
$1 + 8 \sqrt{3}$

Answer 2

Here is your answer

x=(√3 +1)/(√3-1)
= (3 + 1 +2√3) / 2
= {2(2+ √3)}/2
= 2+√3

y= (√3-1)/(√3+1)
= (3+1-2√3)/ 2
= {2(2-√3)}/2
= 2-√3
so, x-y= 2+√3-2+√3= 2√3
x+y= 2+√3+2-√3=4

so, x^2+xy-y^2
= (x+y)(x-y)+xy
= (4×2√3)+(4-3)
= 8√3 + 1 (Answer)

Hope it helps