Question

Como Resolver 4x⁴ - 1= 0 ????????????

Answer 1

4x⁴ - 1 = 0
4x⁴ = 1
$x^4 \ = \ \frac{1}{4}$

$x \ = \ \sqrt[4]{\frac{1}{4}}$

$x \ = \ \frac{1}{\sqrt[4]{4}}$


Racionalizando:

$x \ = \ \frac{1}{\sqrt[4]{4}} \ . \ \frac{\sqrt[4]{4^3}}{\sqrt[4]{4^3}}$

$x \ = \ \frac{\sqrt[4]{4^3}}{\sqrt[4]{4 \ .\ 4^3}}$

$x \ = \ \frac{\sqrt[4]{4^{3}}}{\sqrt[4]{4^4}}$

$x \ = \ \frac{\sqrt[4]{4^{3}}}{\sqrt[\not{4}]{4^{\not{4}}}}$

$x \ = \ \frac{\sqrt[4]{4^{3}}}{4}$

$x \ = \ \frac{4^{\frac{3}{4}}}{4}$

$x \ = \ 4^{\frac{3}{4}} \ . \ \frac{1}{4}$

$x \ = \ 4^{\frac{3}{4}} \ . \ 4^{-1}$

$x \ = \ 4^{\frac{3}{4} \ + \ (-1)}$

$x \ = \ 4^{\frac{3}{4} \ - \ 1}$



MMC:

$x \ = \ 4^{\frac{3 \ - \ 4}{4}}$

$x \ = \ 4^{-\frac{1}{4}}$

$x \ = \ (\frac{1}{4})^{\frac{1}{4}}$

$\boxed{\bol{x \ = \ \frac{1}{4^{\frac{1}{4}}}}}$