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Let the diameter of a subset S of the p...

Let the diameter of a subset S of the plane be defined as the maximum of the distance between arbitrary pairs of points of S.
Q. Let `S={(x,y):(sqrt(5)-1)x-sqrt(10+2sqrt(5))y ge 0, (sqrt(5)-1)x+sqrt(10+12sqrt(5)) y ge 0, x^(2)+y^(2) le 9}` then the diameter of S is :

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Let the diameter of a subset S of the plane be defined as the maximum of the distance between arbitrary pairs of points of S. Q. Let S={(x,y):(y-x) le 0, x+y ge 0, x^(2)+y^(2) le 2} then the diameter of S is :

Let the diameter of a subset S of the plane be defined as the maximum of the distance between arbitrary pairs of points of S. Q. Let S={(x,y):(y-x) le 0, x+y ge 0, x^(2)+y^(2) le 2} then the diameter of S is :

sqrt(2)x + sqrt(3)y=0 sqrt(5)x - sqrt(2)y=0

x=sqrt(2+sqrt(5))+sqrt(2-sqrt(5)) and y=sqrt(2+sqrt(5))-sqrt(2-sqrt(5)) then evaluate x^(2)+y^(2)

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}

If x=(sqrt(5)+1)/(sqrt(5)-1) and y=(sqrt(5)-1)/(sqrt(5)+1) find the value of x^(2)+y^(2)

If (2+sqrt(5))/(2-sqrt(5)) =x and (2-sqrt(5))/(2+sqrt(5)) =y , find the value of x^(2)-y^(2) .

(2)/(sqrt(3)+sqrt(5))+(5)/(sqrt(3)-sqrt(5))=x sqrt(3)+y sqrt(5)

If x =(sqrt(5)-2)/(sqrt(5)+2) and y = (sqrt(5)+2)/(sqrt(5)-2) : find : x^(2)+ y^(2)+xy