Question
Wed September 25, 2013 By: Sthitaprajna Mishra

Sir, the question is:

Expert Reply
Wed September 25, 2013

Let (2+?5)1/2 = a

and (2-?5)1/2 = b

x=(2+?5)1/2+(2-?5)1/2

Squaring both sides

x2=(2+?5)1/2* 2+(2-?5)1/2* 2+ 2((2+?5)(2-?5))1/2

=2+?5+2-?5+2(22-?52)1/2

=4+2(22-?52)1/2                              ...(1)

y=(2+?5)1/2-(2-?5)1/2

Squaring both sides

y2=(2+?5)1/2* 2+(2-?5)1/2* 2- 2((2+?5)(2-?5))1/2

=2+?5+2-?5-2(22-?52)1/2

=4-2(22-?52)1/2                             ...(2)

Adding (1) and (2):

x2+y2=4+2(22-?52)1/2+ 4-2(22-?52)1/2 = 4 + 4 = 8

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