Question

Find the value of a and b in the following:

`1/(3 + sqrt(7)) = a + bsqrt(7)`

Answer 1

We are given:

`1/(3 + sqrt(7)) = a + bsqrt(7)`

Step 1: Rationalise the denominator

Multiply numerator and denominator by the conjugate `(3 - sqrt(7))`:

`1/(3 + sqrt(7)) = (3 - sqrt(7))/((3 + sqrt(7))(3 - sqrt(7))`

Step 2: Simplify

Denominator: `3^2 - (sqrt(7))^2`

= 9 – 7

= 2

Numerator: `3 - sqrt(7)`

So, `1/(3 + sqrt(7)) = (3 - sqrt(7))/2`

= `3/2 - 1/2 sqrt(7)`

`a = 3/2, b = -1/2`