Find the value of a and b

5+✓3/7-4✓3=a+✓3b

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Solution

(5+✓3) / (7-4✓3) = a+✓3b
(5+✓3)(7+4✓3) / (7-4✓3)(7+4✓3) = a+✓3b [Rationalizing the denominator]
(35+20✓3+7✓3+12) / (49-48) = a+✓3b
(47+27✓3) / 1 = a+✓3b
47 + 27✓3 = a + ✓3b

By comparing LHS and RHS,

a = 47, b = 27

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