Advertisements
Advertisements
प्रश्न
In the following determine rational numbers a and b:
`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`
Advertisements
उत्तर
We know that rationalization factor for `sqrt11 + sqrt7` is `sqrt11 - sqrt7`. We will multiply numerator and denominator of the given expression `(sqrt11 - sqrt7)/(sqrt11 + sqrt7)` by `sqrt11 - sqrt7` to get
`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) xx (sqrt11 - sqrt7)/(sqrt11 - sqrt7) = ((sqrt11)^2 + (sqrt7)^2 - 2 xx sqrt11 xx sqrt7)/(sqrt(11)^2 - sqrt(7)^2)`
`= (11 + 7 - 2 sqrt77)/(11 - 7)`
`= (18 - 2sqrt77)/4`
`= 9/2 - 1/2 sqrt77`
On equating rational and irrational terms, we get
`a - bsqrt77 = 9/2 - 1/2 sqrt77`
Hence we get a = 9/2, b = 1/2
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`3/sqrt10`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to
If x = \[\sqrt{5} + 2\],then \[x - \frac{1}{x}\] equals
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
