If X = 2√3 + 2√2 , Find : X + 1/X - Mathematics

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`

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Rationalisation of Surds

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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.

`3 /sqrt5`

Write the simplest form of rationalising factor for the given surd.

`sqrt 27`

Write the simplest form of rationalising factor for the given surd.

`4 sqrt 11`

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

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 : y²

Show that :
`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`

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

Rationalise the denominator `1/sqrt(50)`

If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`