Question

find the value of a and b if ​

Answer 1

Answer:

Step-by-step explanation:

.

Answer 2

Answer:

Required value of a is 9 / 11 and b is 19 / 11.

Step-by-step explanation:

Given,

$\dfrac{3-\sqrt5}{3+2\sqrt5}=a\sqrt5-b$

Using Rationalisation : Multiplying as well dividing ( side contain irritation number, here that side is left hand side ) by the original denominator with opposite sign between the rational and irrational numbers.

So, here we have to multiply as well divide by 3 - 2√5 .

$\implies \dfrac{3-\sqrt5}{3+2\sqrt5}\times\dfrac{3-2\sqrt5}{3-2\sqrt5}=a\sqrt5-b\\\\\\\implies \dfrac{(3-\sqrt5)(3-2\sqrt5)}{(3+2\sqrt5)(3-2\sqrt5)}=a\sqrt5-b$

From the properties of expansion :

• ( a + b )( a - b ) = a^2 - b^2

$\implies\dfrac{3(3-2\sqrt5)-\sqrt5(3-2\sqrt5)}{(3)^2-(2\sqrt5)^2}=a\sqrt5-b \\\\\\\implies\dfrac{9-6\sqrt5-3\sqrt5+10}{9-20}=a\sqrt5-b \\\\\\\implies \dfrac{19-9\sqrt5}{-11}=a\sqrt5-b\\\\\\\implies\dfrac{ 9\sqrt5}{11}-\dfrac{19}{11}=a\sqrt5-b$

Comparing both sides :

a = 9 / 11

b = 19 / 11

Hence the required value of a is 9 / 11 and b is 19 / 11.