Question

If k=[√(44+24√2)+√(11-6√2)]/(√2+1)​

Answer 1

Answer:

k = ±3  or  ±(8√2 - 7)

Step-by-step explanation:

If k=[√(44+24√2)+√(11-6√2)]/(√2+1)​

44 + 24√2

= 8 + 36 + 24√2

= (2√2)² + 6² + 2(2√2)6

= (6 + 2√2)²

=> [√(44+24√2) = ±(6 + 2√2)

11-6√2

= 9 + 2 - 6√2

= 3² + √2²  - 2(3)(√2)

= ( 3 - √2)²

=> √(11-6√2) = ± (3 - √2)

=> Numerator = ±(6 + 2√2)  ± (3 - √2)

= ±(9 + √2)    or ±(3 + 3√2)  or

±(3 + 3√2)/(√2+1)​) =  ±3

=> k = ±3

or ±(9 + √2)/(√2+1)​)

= ±(9 + √2)/(√2+1)​)   * (√2-1/)/(√2-1)

= ±(9√2 - 9 + 2 - √2)

= ±(8√2 - 7)