Advertisements
Advertisements
प्रश्न
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
उत्तर
We have, `(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
For rationalising the above equation, we multiply numerator and denominator of LHS by `3 - 2sqrt(5)`, we get
⇒ `((3 - sqrt(5)))/(3 + 2sqrt(5)) xx (3 - 2sqrt(5))/(3 - 2sqrt(5)) = asqrt(5) - 19/11`
⇒ `(3(3 - 2sqrt(5)) - sqrt(5)(3 - 2sqrt(5)))/((3)^2 - (2sqrt(5))^2) = asqrt(5) - 19/11` ...[Using identity, (a – b)(a + b) = a2 – b2]
⇒ `(9 - 6sqrt(5) - 3sqrt(5) + 10)/(9 - 4 xx 5) = asqrt(5) - 19/11`
⇒ `(19 - 9sqrt(5))/(9 - 20) = asqrt(5) - 19/11`
⇒ `(19 - 9sqrt(5))/(-11) = asqrt(5) - 19/11`
⇒ `(9sqrt(5))/11 - 19/11 = asqrt(5) - 19/11`
⇒ `(9sqrt(5))/11 = asqrt(5)`
⇒ `a = 9/11`
APPEARS IN
संबंधित प्रश्न
Rationalise the denominator of the following
`sqrt2/sqrt5`
Rationalise the denominator of the following
`(3sqrt2)/sqrt5`
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`
`2/sqrt3`
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
Write the rationalisation factor of \[\sqrt{5} - 2\].
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
