Question

A=√(6-√11) and B=√(6+√11) then find out A+B

Answer 1

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

therefore, value of (A + B) is √22.

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