Advertisements
Advertisements
प्रश्न
If `[ 2 + sqrt5 ]/[ 2 - sqrt5] = x and [2 - sqrt5 ]/[ 2 + sqrt5] = y`; find the value of x2 - y2.
उत्तर
x =`[ 2 + sqrt5 ]/[ 2 - sqrt5]`
=`[ 2 + sqrt5 ]/[ 2 - sqrt5] xx [ 2 + sqrt5 ]/[ 2 + sqrt5] `
=`[( 2 + sqrt5)^2]/[2^2 - (sqrt5)^2]`
=`( 4 + 4sqrt5 + 5)/(4 - 5)`
=`( 9 + 4sqrt5)/ -1`
= `- ( 9 - 4sqrt5)`
y = `[2 - sqrt5 ]/[ 2 + sqrt5]`
=`[ 2 - sqrt5 ]/[ 2 + sqrt5] xx [ 2 - sqrt5 ]/[ 2 - sqrt5] `
=`[( 2 - sqrt5)^2]/[2^2 - (sqrt5)^2]`
=`( 4 - 4sqrt5 + 5)/(4 - 5)`
=`( 9 - 4sqrt5 )/ -1`
=` - ( 9 + 4sqrt5 )`
∴ ` x^2 - y^2 = ( - 9 - 4sqrt5 )^2 - ( - 9 + 4sqrt5 )^2`
= `81 + 72sqrt5 + 80 - ( 81 - 72sqrt5 + 80)`
= `81 + 72sqrt5 + 80 - 81 + 72sqrt5 - 80`
= `144sqrt5`
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`3 /sqrt5`
Rationalize the denominator.
`6/(9sqrt 3)`
Write the simplest form of rationalising factor for the given surd.
`sqrt 27`
Write the lowest rationalising factor of : √5 - √2
Write the lowest rationalising factor of : 3√2 + 2√3
Find the values of 'a' and 'b' in each of the following:
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`
If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :
x2
Rationalise the denominator `1/sqrt(50)`
Rationalise the denominator and simplify `(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`
Rationalise the denominator and simplify `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6))`
