Question

If x= 3 +2√2, then check whether x + 1/x is rational or irrational​

Answer 1

Answer:

rational

Step-by-step explanation:

x= 3+2√2

$\frac{1}{x} =\frac{1}{3+2\sqrt{2}} \\\\ rationalising \ factor=3-2\sqrt{2} \\\\ \frac{1}{x} =\frac{1}{3+2\sqrt{2}} \times \frac{3-2\sqrt{2}}{3-2\sqrt{2}} \\\\ \frac{1}{x} =\frac{3-2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})} \\\\ \frac{1}{x} =\frac{3-2\sqrt{2}}{3^2-(2\sqrt{2})^2} \\\\ \frac{1}{x} =\frac{3-2\sqrt{2}}{9-4(2)} \\\\ \frac{1}{x} =\frac{3-2\sqrt{2}}{9-8} \\\\ \frac{1}{x} =\frac{3-2\sqrt{2}}{1} \\\\ \frac{1}{x} =3-2\sqrt{2}$

→ x + 1/x = 3 + 2√2 + 3 - 2√2

             = 6      [ rational number ]