Question

find the value of a and b if 3+✓7 /3-✓7 = a+b ✓7​

Answer 1

Answer: a = 8 ; b = 3

Given that,

$\dfrac{ 3 + \sqrt{7} }{ 3 - \sqrt{7} } = a + b\sqrt{7}$

We are required to find the values of 'a' & 'b'

Solution:

Let's first Rationalise the given information.

$\implies \dfrac{ 3 + \sqrt{7}}{3 - \sqrt{7}} \times \dfrac{3 + \sqrt{7}}{3 + \sqrt{7}}\\\\\\\implies \dfrac{ (3+ \sqrt{7})^2}{(3)^2 - (\sqrt{7})^2}\\\\\\\implies \dfrac{ 9 + 7 + 2(3)(\sqrt{7})}{9 - 7}\\\\\\\implies \dfrac{16 + 6\sqrt{7}}{2}\\\\\\\implies \boxed{ 8 + 3\sqrt{7}}$

Now comparing the coefficients of the final term with the RHS we get:

→ 8 + 3√7 = a + b√7

This implies,

• a = 8
• b = 3

Hence value of 'a' = 8 and 'b' = 3.