Advertisements
Advertisements
प्रश्न
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
उत्तर
`(3 + sqrt(7))/(3 - sqrt(7)`
= `(3 + sqrt(7))/(3 - sqrt(7)) xx (3 + sqrt(7))/(3 + sqrt(7)`
= `(3 + sqrt(7))^2/((3)^2 - (sqrt(7))^2`
= `(9 + 6sqrt(7) + 7)/(9 - 7)`
= `(16 + 6sqrt(7))/(2)`
= `8 + 3sqrt(7)`
= `"a" + "b"sqrt(7)`
Hence, a = 8 and b = 3.
APPEARS IN
संबंधित प्रश्न
Simplify by rationalising the denominator in the following.
`(1)/(5 + 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.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
In the following, find the value of a and b:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
