Question

X=2+√3 show that X2+1/X2=14

Answer 1

Solution:

i ) Given x = 2+√3 ---(1)

ii ) 1/x = 1/(2+√3)

Rationalising the denominator, we get

= (2-√3)/[(2+√3)(2-√3)]

= (2-√3)/[2²-(√3)²]

= (2-√3)/(4-3)

= (2-√3)----(2)

iii ) x + 1/x

= 2+√3+2-√3

= 4 ----(3)

Now ,

x²+1/x²

= (x+1/x)² - 2

= 4² - 2

= 16 -2

= 14

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