Question

√√√x =⁴√⁴√⁴√3x⁴+4, then the value of x⁴ is

Answer 1

$\textbf{Given:}$

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

$\textbf{To find:}$

$\text{The value of x^4 }$

$\textbf{Solution:}$

$\text{Consider,}$

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

$\text{This can be written as}$

$((x^\frac{1}{2})^\frac{1}{2})^\frac{1}{2}=(((3x^4+4)^\frac{1}{4})^\frac{1}{4})^\frac{1}{4}$

$x^{\frac{1}{2}{\times}\frac{1}{2}{\times}\frac{1}{2}}=(3x^4+4)^{\frac{1}{4}{\times}\frac{1}{4}{\times}\frac{1}{4}$

$x^\frac{1}{8}=(3x^4+4)^\frac{1}{64}$

$\text{Raising bothsides to the power 64}$

$x^\frac{64}{8}=(3x^4+4)^\frac{64}{64}$

$x^8=3x^4+4$

$x^8-3x^4-4=0$

$x^8-4x^4+x^4-4=0$

$x^4(x^4-4)+1(x^4-4)=0$

$(x^4+1)(x^4-4)=0$

$\implies\bf\,x^4=4,-1$

$\textbf{Answer:}$

$\textbf{The value of \bf\,x^4 is 4 or -1}$

Find more:

If 5^x-1 + 5^x+1=650 then find x​

https://brainly.in/question/11573395#