If-a-1-a-23-then-a-1-4-1-a-1-4-

Question Number 136614 by bemath last updated on 24/Mar/21

I f a + \frac{1}{a} = 23 t h e n \sqrt[4]{a} + \frac{1}{\sqrt[4]{a}} = ?

Answered by mr W last updated on 24/Mar/21

a + \frac{1}{a} = {(\sqrt{a} + \frac{1}{\sqrt{a}})}^{2} - 2 = 23

\sqrt{a} + \frac{1}{\sqrt{a}} = 5

{(\sqrt[4]{a} + \frac{1}{\sqrt[4]{a}})}^{2} - 2 = 5

\sqrt[4]{a} + \frac{1}{\sqrt[4]{a}} = \sqrt{7}

Commented by bemath last updated on 24/Mar/21

o r \pm \sqrt{7} ?

Commented by mr W last updated on 24/Mar/21

n o! w i t h o u t m i n u s!

\sqrt[4]{a} > 0 j u s t l i k e \sqrt{a} > 0

Commented by bemath last updated on 24/Mar/21

g r e a t s i r

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