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`
Write the simplest form of rationalising factor for the given surd.
`sqrt 32`
Write the simplest form of rationalising factor for the given surd.
`3 sqrt 72`
Write the lowest rationalising factor of √5 - 3.
Write the lowest rationalising factor of 15 – 3√2.
If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find m2
If x = 2√3 + 2√2, find: `(x + 1/x)`
If x = 5 - 2√6, find `x^2 + 1/x^2`
Show that :
`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`
Rationalise the denominator `sqrt(75)/sqrt(18)`
