Question

If a=4/3-√5 find the value of a+4/a

Answer 1

$6 - 2 \sqrt{5} \: answer$

Answer 2

Answer:

The value of the expression is $-\frac{1}{87}(28+195\sqrt{5})$.

Step-by-step explanation:

The given expression is

$a+\frac{4}{a}$

The value of a is $\frac{4}{3}-\sqrt{5}$.

$a+\frac{4}{a}=\frac{4}{3}-\sqrt{5}+\frac{4}{\frac{4}{3}-\sqrt{5}}$

$a+\frac{4}{a}=\frac{4}{3}-\sqrt{5}+\frac{4}{\frac{4}{3}-\sqrt{5}}\times \frac{\frac{4}{3}+\sqrt{5}}{\frac{4}{3}+\sqrt{5}}$

$a+\frac{4}{a}=\frac{4}{3}-\sqrt{5}+\frac{4(\frac{4}{3}+\sqrt{5}))}{(\frac{4}{3})^2-(\sqrt{5})^2}$

$a+\frac{4}{a}=\frac{4}{3}-\sqrt{5}+\frac{\frac{16}{3}+4\sqrt{5}))}{\frac{16}{9}-5}$

$a+\frac{4}{a}=-\frac{1}{87}(28+195\sqrt{5})$

Therefore the value of the expression is $-\frac{1}{87}(28+195\sqrt{5})$.