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refer the attachment!
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Given,
x = root 3 + root 2/ root 3 - root 2
y = root 3 - root 2 / root 3 + root 2
thus, x+y = ( root 3 + root 2/ root 3 - root 2 ) + (root 3 - root 2 / root 3 + root 2)
= ( root 3 + root 2)2 + ( root 3 - root 2)2 /( root 3 - root 2)* ( root 3 - root 2)
= {3 + 2 + 2(root 3 * root 2) + 3 + 2 - 2 ( root 3* root 2)} /( root 3) 2-(root 2)2
= ( 3+ 2 + 3 + 2)/ 3 - 2
= 10 / 1
= 10
thus, ( x+y) ^ 2 = ( 10) ^ 2 = 100
Thus, x2 + y2 + 2xy = 100
Now, you can find the value of x2 + y2 + xy on your own...
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