Question

if x=3+✓2 find x+1/x​

Answer 1

Solution:

i) x = 3+√2 ---(1)

ii)1/x = 1/(3+√2)

Rationalising the denominator,we get

= (3-√2)/[(3+√2)(3-√2)]

= (3-√2)/[3²-(√2)²]

= (3-√2)/(9-2)

= (3-√2)/7 ----(2)

Now ,

x + 1/x

= 3+√2 + (3-√2)/7

= [7(3+√2)+3-√2)]/7

= (21+7√2+3-√2)/7

= (24+6√2)/7

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