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(a+ 1/a +2)^2 = 4
square roting both sides
(a +1/a +2) = +/- 2
case 1
a + 1/a + 2 = 2
a + 1/a = 0
squaring both sides
a^2 + 1/a^2 + 2 = 0
a^2 + 1/a^2 = -2
not possible as per question
case2
a + 1/a + 2 = -2
a + 1/a = -4
squaring both sides
a^2 + 1/a^2 + 2 = 16
a^2 + 1/a^2 = 14
hence answer = 14
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