a=2+√3 and 1/a of value
Answers
Answer:
Here is the answer you were looking for:
\begin{gathered}a = 2 + \sqrt{3} \\ \\ \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\ \end{gathered}
a=2+
3
a
1
=
2+
3
1
On rationalizing the denominator we get,
\begin{gathered} \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \end{gathered}
a
1
=
2+
3
1
×
2−
3
2−
3
Using the identity :
(x + y)(x - y) = {x}^{2} - {y}^{2} (x+y)(x−y)=x
2
−y
2
\begin{gathered} \frac{1}{a} = \frac{2 - \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3} )}^{2} } \\ \\ \frac{1}{a} = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \frac{1}{a} = 2 - \sqrt{3} \\ \\ a - \frac{1}{a} \end{gathered}
a
1
=
(2)
2
−(
3
)
2
2−
3
a
1
=
4−3
2−
3
a
1
=2−
3
a−
a
1
Putting the values,
\begin{gathered}a - \frac{1}{a} = (2 + \sqrt{3} ) - (2 - \sqrt{3} ) \\ \\ a - \frac{1}{a} = 2 + \sqrt{3} - 2 + \sqrt{3} \\ \\ a - \frac{1}{a} = \sqrt{3} + \sqrt{3} \\ \\ a - \frac{1}{a} = 2 \sqrt{3} \end{gathered}
a−
a
1
=(2+
3
)−(2−
3
)
a−
a
1
=2+
3
−2+
3
a−
a
1
=
3
+
3
a−
a
1
=2
3
Hope this helps!!!
Answer:
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