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Question

If x=(2+5)1/2+(52)1/2 and y=(2+5)1/2(52)1/2,then evaluate x2+y2.

Solution
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a b
x=(2+5)1/2+(52)1/2
y=((2+5))1/2(52)1/2
i.e x=a1/2+b1/2
y=a1/2b1/2
So x2+y2=a+b+2a1/2b1/2
+a+b2a1/2b1/2
=2(a+b)
=2(2+5+52)
=2.25
=45

1161868_866909_ans_a0f9ed05571e4ca3a6219a9ae5a7da84.jpg

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