Find $\displaystyle{ \frac{2}{1 + 2\sqrt{3}} + \frac{3}{2 - \sqrt{3}}}$, and write your answer in the form $\displaystyle \frac{A + B\sqrt{3}}{C}$, with the fraction in lowest terms and $A > 0$. What is $A+B+C$?
+130462
Convert :$21+2√3+32−√3$
To the form : $A+B√3C$
Where $A>0$
And find $A+B+C$?
[ 2 * (2 - √3) + 3 ( 1 + 2√3) ] / [ ( 1 + 2 √3) ( 2 - √3) ] =
[ 4 - 2√3+ 3 + 6√3 ] / [ 2 + 4√3 - √3 - 6 ] =
[ 7 + 4√3 ] / [ 3√3 - 4]
[ 7 + 4√3 ] * [ 3√3 + 4] / [ ( 3√3 - 4) (3√3 + 4 ) ]
[ 21√3 + 36 + 28 + 16√3] / [ 27 - 16 ]
[ 64 + 37√3] / 11
So..... A = 64, B = 37 , C = 11
So
A + B + C = 112
