If X =Sqrt5 - 2/Sqrt5 + 2 and Y = Sqrt5 + 2/ Sqrt5 - 2 Find : Xy - Mathematics

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

Sum

xy = `[(sqrt5 - 2)(sqrt5 + 2)]/[(sqrt5 + 2)(sqrt5 - 2)] = 1`

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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 6.3 | Page 22

Rationalize the denominator.

`6/(9sqrt 3)`

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

`3/5 sqrt 10`

Write the lowest rationalising factor of : √5 - √2

Write the lowest rationalising factor of : √13 + 3

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

x² + y² + xy.

If x = 5 - 2√6, find `x^2 + 1/x^2`

Evaluate : `( 4 - √5 )/( 4 + √5 ) + ( 4 + √5 )/( 4 - √5 )`

Rationalise the denominator `sqrt(75)/sqrt(18)`

Rationalise the denominator and simplify `(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`

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