If (5+√3)/(7-4√3) = 47a +√(3 )b, find the values of a and b.
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Given, (5+√3)/(7-4√3)
= (5+√3)/(7-4√3)/(7+4√3)/(7+4√3)
= (5+√3)(7+4√3)/(7-4√3)^2
= 35+20√3+7√3+12/(7)²-(4√3)²
= 35+20√3+7√3+12/1
= 47+27√3/1
= 47+27√3
=47a+√3b
So, a = 1, b = 27
Hope this helps!
= (5+√3)/(7-4√3)/(7+4√3)/(7+4√3)
= (5+√3)(7+4√3)/(7-4√3)^2
= 35+20√3+7√3+12/(7)²-(4√3)²
= 35+20√3+7√3+12/1
= 47+27√3/1
= 47+27√3
=47a+√3b
So, a = 1, b = 27
Hope this helps!
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