If `x=(sqrt3+sqrt2)/(sqrt3-sqrt2)andy=(sqrt3-sqrt2)/(sqrt3+sqrt2)` then find the value of `x^(2)+y^(2)` ?

Explanation

`given , a=(3+sqrt5)/2`
`1/a=2/(3+sqrt5)=2/(3+sqrt5)xx(3-sqrt5)/(3-sqrt5)`
[multiplying numerator and denominator by `3-sqrt5`)
`(6-2sqrt5)/(3^(2)-(sqrt5)^(2)) " " ["using identity" , (a-b)(a+b)=a^(2)-b^(2)]`
`(6-2sqrt5)/(9-5)=(6-2sqrt5)/4`
`1/a=(2(3-sqrt5))/4=(3-sqrt5)/2`
`a^(2)+1/(a^(2))a^(2)+1/a^(2)+2-2=(a+1/a)^(2)-2" " ["adding and subtarcting2"]`
`((3+sqrt5)/2+(3-sqrt5)/2)^(2)-2 " " ["from Eqs. (i)and (ii)"]`
`(6/2)^(2)-2=(3)^(2)-2=9-2=7`