Question

if a and b are rational number and 3+ root 5 / 3- root 5 = a+b root 5 , find the values of a and b

Answer 1

Hello Mate!

On Rationalizing we get,

$\frac{3 + \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ = \frac{ {(3 + \sqrt{5} )}^{2} }{9 - 5} \\ = \frac{9 + 5 + 6 \sqrt{5} }{4} \\ \frac{7 + 3 \sqrt{5} }{2} = a + b \sqrt{5}$

On comparing both sides we get,

a = 7/2 and b = 3/2

Hope it helps☺!✌

Answer 2

Answer:

Hello Mate!

On Rationalizing we get,

\begin{lgathered}\frac{3 + \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ = \frac{ {(3 + \sqrt{5} )}^{2} }{9 - 5} \\ = \frac{9 + 5 + 6 \sqrt{5} }{4} \\ \frac{7 + 3 \sqrt{5} }{2} = a + b \sqrt{5}\end{lgathered}3−53+5×3+53+5=9−5(3+5)2=49+5+6527+35=a+b5

On comparing both sides we get,

a = 7/2 and b = 3/2

Hope it help