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# In the Following Determine Rational Numbers a and B: (Sqrt11 - Sqrt7)/(Sqrt11 + Sqrt7) = a - Bsqrt77 - CBSE Class 9 - Mathematics

ConceptOperations on Real Numbers

#### 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

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