if a=2-root3, find (a-1/a)3
Answers
Answer:please mark it as brainliest
The value of given expression is 2\sqrt{3}2
3
.
Step-by-step explanation:
It is given that
a=2+\sqrt{3}a=2+
3
We have to find the value of a-\frac{1}{a}a−
a
1
.
a-\frac{1}{a}=2+\sqrt{3}-\frac{1}{2+\sqrt{3}}a−
a
1
=2+
3
−
2+
3
1
a-\frac{1}{a}=2+\sqrt{3}-\frac{1}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}a−
a
1
=2+
3
−
2+
3
1
×
2−
3
2−
3
a-\frac{1}{a}=2+\sqrt{3}-\frac{2-\sqrt{3}}{2^2-(\sqrt{3})^2}a−
a
1
=2+
3
−
2
2
−(
3
)
2
2−
3
a-\frac{1}{a}=2+\sqrt{3}-\frac{2-\sqrt{3}}{4-3}a−
a
1
=2+
3
−
4−3
2−
3
a-\frac{1}{a}=2+\sqrt{3}-\frac{2-\sqrt{3}}{1}a−
a
1
=2+
3
−
1
2−
3
a-\frac{1}{a}=2+\sqrt{3}-2+\sqrt{3}a−
a
1
=2+
3
−2+
3
a-\frac{1}{a}=2\sqrt{3}a−
a
1
=2
3
Therefore the value of given expression is 2\sqrt{3}2
3
.