Math, asked by Azux, 4 months ago

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Answered by sharmaharshita1307
2

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Answered by KokilaAbhishek
0

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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