Question

plz answer. Its urgent. thanks​

Answer 1

Answer:

$a = \dfrac{5}{18}$

$b = -\dfrac{1}{18}$

Step-by-step explanation:

You need to rationalize the fraction.

$\dfrac{1}{5 + \sqrt{7}} = a + b\sqrt{7}$

$\dfrac{1}{5 + \sqrt{7}} \times \dfrac{5 - \sqrt{7}}{5 - \sqrt{7}} = a + b\sqrt{7}$

$\dfrac{5 - \sqrt{7}}{25 - 7} = a + b\sqrt{7}$

$\dfrac{5 - \sqrt{7}}{18} = a + b\sqrt{7}$

$\dfrac{5}{18} - \dfrac{1}{18}\sqrt{7} = a + b\sqrt{7}$

$a = \dfrac{5}{18}$

$b = -\dfrac{1}{18}$