Advertisements
Advertisements
प्रश्न
Rationalise the denominator of `1/[ √3 - √2 + 1]`
Advertisements
उत्तर
`1/[ √3 - √2 + 1]`
= `1/[(√3 - √2) + 1] xx [(√3 - √2) - 1]/[(√3 - √2) - 1]`
= `(√3 - √2 - 1)/[(√3 - √2)^2 - (1)^2]`
= `(√3 - √2 - 1)/[(√3)^2 - 2√6 + (√2)^2 - 1 ]`
= `(√3 - √2 - 1)/(3 - 2√6 + 2 - 1)`
= `(√3 - √2 - 1)/( 4 - 2√6 )`
= `[(√3 - √2) - 1]/[2( 2 - √6 )]`
= `[ √3 - √2 - 1 ]/[ 2( 2 - √6 ) ] xx [ 2 + √6 ]/[ 2 + √6 ]`
= `[ 2√3 - 2√2 - 2 + √18 - √12 - √6 ]/[ 2[ (2)^2 - ( √6)^2 ] ]`
= `[ 2√3 - 2√2 - 2 + 3√2 - 2√3 - √6 ]/[ 2[ 4 - 6] ]`
= `[ √2 - 2 - √6 ]/[ 2(-2) ]`
= `[ √2 - 2 - √6 ]/[ -4 ]`
= `1/4(2 + √6 - √2)`
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
Rationalize the denominator.
`2/(3 sqrt 7)`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
