Question

5+√3/√5-√3=1/2*a+3b√15 What is the value of a and b

Answer 1

its just like your question on this basis you sol it ok
Given  (√3 - 1) / (√3 + 1)         ( rationalize numarator and denominator(√3 - 1) )
⇒ (√3 - 1)(√3 - 1) / (√3 + 1)(√3 - 1)
⇒ (√3 - 1)2 / (3 - 1)
⇒ (3 + 1-2√3 ) / 2
⇒ (2 -√3 )  = a+b√3  ⇒ a = 2 and b = -1
Sol2) :           
Given  (√2 + √3) / (3√2-2√3)     ( rationalize numarator and denominator (3√2 + 2√3 ) )
⇒ (√2 + √3)(3√2 + 2√3 ) / (3√2-2√3)(3√2 + 2√3 )
⇒ (12 + 5√6) / (18-12)
⇒ (2 + (5√6) /6 )  = a-b√6
a = 2 and b = -5/6.

Answer 2

Answer:

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