Question

5+√3/√5-√3 = 1/2a+3b√15
find the value of a and b
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Answer 1

Answer:

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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.

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