#### Question

In the following determine rational numbers *a* and *b*:

`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`

#### Solution

We know that rationalization factor for `sqrt11 + sqrt7` is `sqrt11 - sqrt7`. We will multiply numerator and denominator of the given expression `(sqrt11 - sqrt7)/(sqrt11 + sqrt7)` by `sqrt11 - sqrt7` to get

`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) xx (sqrt11 - sqrt7)/(sqrt11 - sqrt7) = ((sqrt11)^2 + (sqrt7)^2 - 2 xx sqrt11 xx sqrt7)/(sqrt(11)^2 - sqrt(7)^2)`

`= (11 + 7 - 2 sqrt77)/(11 - 7)`

`= (18 - 2sqrt77)/4`

`= 9/2 - 1/2 sqrt77`

On equating rational and irrational terms, we get

`a - bsqrt77 = 9/2 - 1/2 sqrt77`

Hence we get a = 9/2, b = 1/2

Is there an error in this question or solution?

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In the Following Determine Rational Numbers a and B: (Sqrt11 - Sqrt7)/(Sqrt11 + Sqrt7) = a - Bsqrt77 Concept: Operations on Real Numbers.

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