Question

3+√5 /2√5 + 3 = a +b√5
find a and b​

Answer 1

Answer:

a= $\frac{-19}{11}$  & b = $\frac{-9}{11}$

Step-by-step explanation:

$\frac{3+\sqrt{5} }{3+2\sqrt{5} }$ = a+b√5

LHS = $\frac{3+\sqrt{5} }{3+2\sqrt{5} } * \frac{3-2\sqrt{5} }{3-2\sqrt{5} }$

= $\frac{(3+\sqrt{5})*(3+2\sqrt{5} )}{3^2-(2\sqrt{5})^2 }$

= $\frac{3*(3+2\sqrt{5})+\sqrt{5}* (3+2\sqrt{5}) }{9-(4*5)}$

= $\frac{9+6\sqrt{5} +3\sqrt{5}+(2*5)}{9-20}$

= $\frac{9+10+9\sqrt{5}}{-11}$

= $\frac{19+9\sqrt{5}}{-11}$

= $\frac{-19}{11} + ( \frac{-9}{11} )\sqrt{5}$ which is equal to a+b√5

=> a= $\frac{-19}{11}$  & b = $\frac{-9}{11}$