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if 2/√3+√5 + 5 /√3-√5 = √3 + b√5,find the value of a and b

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Raghunath answered 4 year(s) ago

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Solve the following:

i.If √3 - 1 / √3 + 1 = a+b√3

ii. If √2 + √3 / 3√2-2√3 = a-b√6

    ( find the value of a and b here)

Class-IX Maths

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Asked by Sanika

Apr 24

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Raghunath , SubjectMatterExpert

Member since Apr 11 2014

Sol1) :             
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.