Question

If a = 5-2√5, then find a+1 / a​

Answer 1

Answer:

then find a+1 / a find length

Answer 2

Step-by-step explanation:

Given:--$\tt a=5-2\sqrt{5}$

To Find:--$\tt\frac{a + 1}{a}$

$\tt \red{ \implies\frac{5-2\sqrt{5}+1}{5-2\sqrt{5}}}$

$\tt\pink{\implies \frac{2(3-\sqrt{5})}{5-2\sqrt{5}}}$

Rationalize the denominator:

$\tt\orange{\implies \frac{2(3-\sqrt{5})}{5-2\sqrt{5}} \cdot \frac{5+2\sqrt{5}}{5+2\sqrt{5}}=\frac{30+12\sqrt{5}-10\sqrt{5}-20}{{5}^{2}-{(2\sqrt{5})}^{2}}}$

$\tt\blue{\implies \frac{2(15+6\sqrt{5}-5\sqrt{5}-10)}{{5}^{2}-{(2\sqrt{5})}^{2}}}$

to 2020.

$\tt\green{\implies \frac{2(5+\sqrt{5})}{25-20}}$

$\tt\purple{\implies \frac{2(5+\sqrt{5})}{5}}$