Question

If a= 5-2 root 6 then find the value of root a - 1/root a

Answer 1

Answer:

2\sqrt2

Step-by-step explanation:

a=5-2√6 ...(1)

$\frac{1}{a}=\frac{1}{5-2 \sqrt{6} } \times\frac{5+2\sqrt{6} }{5+2\sqrt{6} } =\frac{5+2\sqrt{6}}{(5-2\sqrt{6})(5+2\sqrt{6})} =\frac{5+2\sqrt{6}}{5 ^2-(2\sqrt{6})^2} =\frac{5+2\sqrt{6}}{25-24} =5+2\sqrt{6}\\a+\frac{1}{a}=5-2\sqrt{6}+5+2\sqrt{6}=10$

$(\sqrt{a}-\frac{1}{\sqrt{a}})^2=(\sqrt{a})^2+(\frac{1}{\sqrt{a}})^2-2 \times \sqrt{a} \times \frac{1}{\sqrt{a}}=a+\frac{1}{a}-2=10-2=8\\\sqrt{a}-\frac{1}{\sqrt{a}}=\sqrt{8}=2\sqrt{2}$