If X =Sqrt5 - 2/Sqrt5 + 2 and Y = Sqrt5 + 2/ Sqrt5 - 2 Find : Y2

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : y²

Sum

y²= `[( sqrt5 + 2 )/( sqrt5 - 2 )]^2 = [ 5 + 4 + 4sqrt5 ]/[ 5 + 4 - 4sqrt5 ] = [ 9 + 4sqrt5 ]/[ 9 - 4sqrt5 ]`

= `[ 9 + 4sqrt5 ]/[ 9 - 4sqrt5 ] xx [ 9 + 4sqrt5 ]/[ 9 + 4sqrt5 ] = ( 9 + 4sqrt5)^2/[(9)^2 - (4sqrt5)^2] = [ 81 + 80 + 72sqrt5 ]/[ 81 - 80 ]`

= `161 + 72sqrt5`

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Rationalisation of Surds

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Chapter 1: Rational and Irrational Numbers - Exercise 1 (C) [Page 21]

Chapter 1 Rational and Irrational Numbers
Exercise 1 (C) | Q 6.2 | Page 21

Write the lowest rationalising factor of √5 - 3.

Write the lowest rationalising factor of : 7 - √7

Write the lowest rationalising factor of : 3√2 + 2√3

Find the values of 'a' and 'b' in each of the following :
`[2 + sqrt3]/[ 2 - sqrt3 ] = a + bsqrt3`

Find the values of 'a' and 'b' in each of the following:
`( sqrt7 - 2 )/( sqrt7 + 2 ) = asqrt7 + b`

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find mn

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.

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

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