Advertisements
Advertisements
Question
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
Advertisements
Solution
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
RELATED QUESTIONS
Simplify the following expressions:
`(3 + sqrt3)(3 - sqrt3)`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to
`1/(sqrt(9) - sqrt(8))` is equal to ______.
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
Simplify:
`(1/27)^((-2)/3)`
