Question

If x=3-2√2 then find the value of x+1/x.

Answer 1

x = 3-2√2

So,

1/x = 1/3-2√2 = 3+2√2/(3-2√2)(3+2√2) = 3+2√2 / 9-8 = 3+2√2

So,

x + 1/x = 3-2√2 + 3+2√2 = 6

Hope this helps you !

The only thing you have to do when you see to manipulate the value of 1/x then rationalise the given term of x

Answer 2

Answer:

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