Final answer:
The question asks to find 'a' and 'b' in an expression involving square roots and rationalization. Upon rationalizing the given expression, 'a' is determined as 6/11 and 'b' as 14/11. However, these values do not match any of the provided options, indicating a discrepancy.
Step-by-step explanation:
To find the value of a and b in the expression 3-√5÷3+2√5=a√5-b÷11, we need to rationalize the denominator.
The original equation can be written as:
(3 - √5) / (3 + 2√5)
To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator:
(3 - √5) * (3 - 2√5) / (3 + 2√5) * (3 - 2√5)
Upon simplifying, we get:
(9 - 6√5 + 5) / (9 - 20)
(14 - 6√5) / -11
-14/11 + (6/11)√5
Comparing this expression to the original equation a√5 - b / 11, we can see that:
a = 6/11 and b = 14/11
However, none of the provided options in the question, A) a = 1, b = 2; B) a = 3, b = 4; C) a = -1, b = -2; D) a = 2, b = 3, match this result. There seems to be an error either in the provided options or the process of rationalization.