If a=2+√5 and b= 1/a
then find a² + b²
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a= 2+√5
squaring on both sides
(a)^2 = (2+√5)^2
a^2= (2)^2 +2(2)(√5) + (√5)^2
a^2 = 4 + 4√5 + 25
a^2 = 29 + 4√5. ------------(i)
b = 1/a
squaring on both sides
b^2 = 1/ a^2
put the value of a^2
b^2 = 1/ (29+ 4√5) -----------(ii)
adding eqn (i) and eqn (ii)
a^2 + b^2 = 29+4√5 + 1/(29+4√5)
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