Question

$find \: a \: and \: b \: if \: \frac{7 + \sqrt{3} }{7 - \sqrt{3} } = a + \sqrt{3}b$
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Answer 1

Answer: a= 26/23 & b= 7/23

Step-by-step explanation:

Taking LHS , 7+√3/7-√3

By Rationalising the denominator,

7+√3/7-√3 × 7+√3/7+√3

= (7+√3)^2 / 7^2 - (√3)^2

= 49+14√3+3 / 46

= 52+14√3 / 46

= 2(26+7√3) / 2×23

By cancelling the common factor 2,we get

26+7√3 / 23

which is equal to a+√3b (as given in question)

=> 26/23 + 7√3/23 = a+√3b

=> a= 26/23 and b= 7/23