Advertisements
Advertisements
प्रश्न
In the following, find the values of a and b.
`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`
Advertisements
उत्तर
`(sqrt(3) - 1)/(sqrt(3) + 1)`
= `(sqrt(3) - 1)/(sqrt(3) + 1) xx (sqrt(3) - 1)/(sqrt(3) - 1)`
= `(sqrt(3) - 1)^2/((sqrt(3))^2 - (1)^2`
= `(3 -2 xx sqrt(3) xx 1 + 1)/(3 - 1)`
= `(4 - 2sqrt(3))/(2)`
= `2 - sqrt(3)`
= `2 + (-1) sqrt(3)`
= `"a" + "b"sqrt(3)`
Hence, a = 2 and b = -1.
APPEARS IN
संबंधित प्रश्न
Rationalise the denominators of : `1/(sqrt3 - sqrt2 )`
Simplify : `sqrt18/[ 5sqrt18 + 3sqrt72 - 2sqrt162]`
Simplify by rationalising the denominator in the following.
`(3sqrt(2))/sqrt(5)`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(5)/(sqrt(7) - sqrt(2))`
Simplify by rationalising the denominator in the following.
`(42)/(2sqrt(3) + 3sqrt(2)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
Show that: `x^2 + 1/x^2 = 34,` if x = 3 + `2sqrt2`
