If a=√(6 − √11) and
b=√(6 + √11), then
what is (a+b)?

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1. Answer:

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   Step-by-step explanation:

   It is given that A = √(6 – √11) , B = √(6 + √11)

   We have to find value out A + B

   Here A = √(6 – √11) ⇒A² = 6 – √11

   B = √(6 + √11) ⇒B² = 6 + √11

   A² + B² = (6 – √11) + (6 + √11) = 12

   ⇒(A + B)² – 2AB = 12

   ⇒(A + B)² – 2√(6 – √11) × √(6 + √11) = 12

   ⇒(A + B)² – 2√[(6 – √11)(6 + √11)] = 12

   ⇒(A + B)² – 2√[6² – (√11)²] = 12

   ⇒(A + B)² – 2√(36 – 11) = 12

   ⇒(A + B)² – 2 × 5 = 12

   ⇒(A + B)² = 12 + 10 = 22

   ⇒(A + B) = √22

   ∴ The value of (A + B) is √22.

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