Question

If a = 5+2 square root 6, then a - 1/a is equal to

Answer 1

here is the answer you can also simplify it

Answer 2

$\huge{\underline{\underline{Answer\::-}}}$

$\underline{\underline{Given\::-}}$

a = 5 $2 \sqrt{6}$

$\underline{\underline{Solution\::-}}$

♦ To find a - $\dfrac{1}{a}$.

• We have to rationalize $\dfrac{1}{a}$

• Then we have Find the Sum

>> Rationalizing

$\dfrac{1}{a}$ = $\dfrac{1}{5 + 2 \sqrt{6}}$

= $\dfrac{1}{5 + 2 \sqrt{6}} \times \dfrac{5- 2 \sqrt{6}}{5 - 2 \sqrt{6}}$

= $\dfrac{5 - 2 \sqrt{6}}{(5 + 2 \sqrt{6}) (5 - 2 \sqrt{6}) }$

= $\dfrac{5 - 2 \sqrt{6}}{(5)^2 - (2 \sqrt{6})^2 }$

= $\dfrac{ 5 - 2 \sqrt{6}}{ 25 - 4 \times 6}$

= $\dfrac{ 5 - 2 \sqrt{6}}{25 - 24 }$

= $\dfrac { 5 - 2 \sqrt{6}}{1}$

= $5 - 2 \sqrt{6}$

♦ Now as we have got the value of $\dfrac{1}{a}$

>> Then Finding the Sum of a - $\dfrac{1}{a}$

= ($5 + 2 \sqrt{6}$) - ($5 - 2 \sqrt{6}$)

= $5 + 2 \sqrt{6}$ - $5 + 2 \sqrt{6}$

= ( 5 - 5 ) + ($2 \sqrt{6} + 2 \sqrt{6}$ )

= (0) + ($4 \sqrt{6}$)

= $4 \sqrt{6}$