Question

pls say fast wrong answers = report

Answer 1

Answer:

$a = - \frac{179}{171} \ , \ b = - \frac{20 \sqrt7}{171}$

Step-by-step explanation:

$\frac{2 + 5 \sqrt7}{2 - 5 \sqrt7} = \frac{2 + 5 \sqrt7}{2 - 5 \sqrt7} \times \frac{2 + 5 \sqrt7}{2 + 5 \sqrt7}$                    $[ \ rationalize \ the \ denominator \ ]$

         $=\frac{(2 + 5 \sqrt7)^2}{(2)^2 -( 5 \sqrt7)^2}$                               $[ \ (a - b)(a+b) = a^2 - b^2 \ ]$

        $=\frac{4 + 25(7) + 20 \sqrt7}{4 - 25(7)}\\\\= \frac{4 + 175 + 20 \sqrt7}{4 - 175} \\\\= \frac{179 + 20 \sqrt7}{- 171} \\\\= \frac{179}{ -171} + \frac{20 \sqrt7}{-171}\\\\= - \frac{179}{ 171} - \frac{20 \sqrt7}{171}$