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Step-by-step explanation:
given,
a=2-√3 .....(I)
1/a=1/2-√3
= 1/2-√3×2+√3/2+√3
= 2+√3/(2)² - (√3)². [ (a+b)(a-b)= a² - b²]
= 2+√3/1
= 2+√3 ......(ii)
Now,
add (I) and (ii) we get,
a+1/a= 2-√3 + 2+√3
= 4
squaring both sides , we get
( a+1/a)² = (4)²
(a)² + (1/a)² + 2×a×1/a = 16
a² + 1/a² + 2 = 16
a² + 1/a² = 16 - 2
a² + 1/a² = 14
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