Question

if a=4/3-root5 find the value of a+4/a

Answer 1

hope it's help you ......

Answer 2

Answer:

$a+\frac{4}{a}=6$

Step-by-step explanation:

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

/* Rationalising the denominator we get ,

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

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

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

$=\frac{4(3+\sqrt{5})}{4}$

$= 3+\sqrt{5}---(1)$

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

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

$=3+\sqrt{5}+3-\sqrt{5}$

$=3+3\\=6$

Therefore,

$a+\frac{4}{a}=6$

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