Question

If a = 2√2 - √7 then a + 1/a is​

Answer 1

Answer:

4√2

Step-by-step explanation:

a = 2√2 - √7

► $\frac{1}{a} = \frac{1}{2\sqrt{2} - \sqrt{7}} = \frac{(2\sqrt{2} + \sqrt{7})}{(2\sqrt{2} - \sqrt{7})(2\sqrt{2} + \sqrt{7})} = \frac{(2\sqrt{2} + \sqrt{7})}{(2\sqrt{2})^2 - (\sqrt{7})^2} =\frac{(2\sqrt{2} + \sqrt{7})}{8 - 7} = 2\sqrt{2} + \sqrt{7}$

Now, a+ 1/a = 2√2 - √7 + 2√2 + √7 = 4√2