If x = 2√3 + 2√2, find: (x+1x)

If x = 2√3 + 2√2, find: `(x + 1/x)`

Sum

`x + 1/x = 2sqrt3 + 2sqrt2 + (√3 - √2)/2`

= `2( sqrt3 + sqrt2 ) + (sqrt3 - sqrt2)/2`

= `(4( sqrt3 + sqrt2) + (sqrt3 - sqrt2))/2`

= `[ 4sqrt3 + 4sqrt2 + sqrt3 - sqrt2 ]/2`

= `[ 5sqrt3 + 3sqrt2 ]/2`

shaalaa.com

Rationalisation of Surds

Is there an error in this question or solution?

Chapter 1: Rational and Irrational Numbers - Exercise 1 (C) [Page 22]

Chapter 1 Rational and Irrational Numbers
Exercise 1 (C) | Q 8.2 | Page 22

Rationalize the denominator.

`6/(9sqrt 3)`

Write the lowest rationalising factor of : √18 - √50

Find the values of 'a' and 'b' in each of the following:
`[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2`

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :
x²

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : xy

If x = 2√3 + 2√2 , find : `( x + 1/x)^2`

If `[ 2 + sqrt5 ]/[ 2 - sqrt5] = x and [2 - sqrt5 ]/[ 2 + sqrt5] = y`; find the value of x² - y².

If √2 = 1.4 and √3 = 1.7, find the value of : `1/(√3 - √2)`

Rationalise the denominator `(3sqrt(5))/sqrt(6)`

Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`.