Advertisements
Advertisements
Question
Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`.
Advertisements
Solution
`(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`
⇒ `((sqrt(7) - 2)(sqrt(7) - 2))/((sqrt(7) + 2)(sqrt(7) - 2)) = asqrt(7) + b`
⇒ `(sqrt(7) - 2)^2/((sqrt(7))^2 - 2^2) = asqrt(7) + b`
`((sqrt(7))^2 - 2(sqrt(7))(2) + 2^2)/(7 - 4) = asqrt(7) + b`
`(7 - 4sqrt(7) + 4)/3 = asqrt(7) + b`
`(11 - 4sqrt(7))/3 = asqrt(7) + b`
`11/3 + (-4 sqrt(7))/3 = asqrt(7) + b`
`acancel(sqrt(7)) = (-4 cancel(sqrt(7)))/3`
∴ a = `(- 4)/3`
`11/3 + (-4)/3 = a + b`
∴ a = `(- 4)/3 and b = 11/3`
∴ The value of a = `(- 4)/3 and b = 11/3`
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`3 /sqrt5`
Rationalize the denominator.
`1/sqrt14`
Write the simplest form of rationalising factor for the given surd.
`sqrt 50`
Find the values of 'a' and 'b' in each of the following:
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`
If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2]`; find:
x2 + y2 + xy.
If x = `2sqrt3 + 2sqrt2`, find: `1/x`
If x = 5 - 2√6, find `x^2 + 1/x^2`
If √2 = 1.4 and √3 = 1.7, find the value of : `1/(√3 - √2)`
Rationalise the denominator `5/(3sqrt(5))`
Rationalise the denominator and simplify `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6))`
