Question

If x=3+2√2, then find whether x+1/x is rational or irrational

Answer 1

Heya !!!

X = 3+2 root 2

1/X = 1/3+ 2 root 2

Rationalizing the denominator 3 + 2 root 2 we get,

1/X = 1/ 3 + 2 root 2 × 3 - 2 root 2/3 - 2root2

1/X = ( 3 - 2 root 2)/ ( 3 + 2 root 2) ( 3 - 2root2)

1/X = ( 3 - 2root 2) / (3)² - ( 2 root2)²

1/X = ( 3 - 2 root 2) / 9 -8

1/X = ( 3 - 2 root 2)

Therefore,

X + 1/X

=> ( 3 + 2 root 2 ) + ( 3 - 2 root 2)

=> ( 3 2 root 2)+ ( 2 root 2)

=> 6 which is rational.

Hence,

X + 1/X is rational

Answer 2

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