Question

if x=3+2√2. find the value of x+1/x​

Answer 1

Answer:

= 6

Step-by-step explanation:

$First,let's \ find \ the \ value \ of \ \frac{1}{x} \\\\x=3+2\sqrt{2} \\\\ \frac{1}{x} =\frac{1}{3+2\sqrt{2}}\\\\ rationalising \ factor=3-2\sqrt{2} \\\\ \frac{1}{x} =\frac{1}{3+2\sqrt{2}}(\frac{3-2\sqrt{2}}{3-2\sqrt{2}} ) \\\\ = \frac{3-2\sqrt{2}}{3^{2}-(2\sqrt{2})^{2}} \ \ \ \ \ \ \ \ [(a-b)(a+b)=a^{2}-b^{2}] \\\\= \frac{3-2\sqrt{2}}{9-4(2)} \\\\=\frac{3-2\sqrt{2}}{9-8} \\\\=\frac{3-2\sqrt{2}}{1} \\\\=3-2\sqrt{2}\\\\\\=>x+\frac{1}{x} = (3+2\sqrt{2})+(3-2\sqrt{2})\\\\ =>x+\frac{1}{x} = 3+3 =6$