Question

7+√5/7-√5 + 7-√5/7+√5 = a + 7/11√5b

Answer 1

The values of a and b in the given surd expression are; a = 27/22 and b = 1/2

How to simplify surds?

The correct expression is;

(7 + √5)/(7 - √5) - (7 - √5)/(7 + √5) = a + (7/11)√5b

Let us first rationalize the denominator of the first term to get;

(7 + √5)/(7 - √5) = [(7 +√5)/(7-√5)] * [(7 + √5)/(7 + √5)]

⇒ (54 + 14√5)/44

⇒ (27/22) + 7(√5)/22

Let us first rationalize the denominator of the second term to get;

[(7 - √5)/(7 + √5)] * [(7 - √5)/(7 - √5)]

⇒ (54 - 14√5)/44

⇒ (27/22) - 7(√5)/22

Thus;

a = 27/22 and b = 1/2

Read more about surds at; https://brainly.com/question/24700530

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