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Chapter 0: Problem 114

Solve each equation, rounding your answer to four significant digits where necessary. $$ x^{4}-81=0 $$

Short Answer

Expert verified
The solutions for the given equation, rounded to four significant digits, are: \(x \approx 3.0000\) and \(x \approx -3.0000\).

Step by step solution

01

Identify the type of equation

The given equation is a polynomial equation of degree 4: \(x^{4}-81=0\).
02

Isolate the term with variable x

To isolate the term with variable x, we first add 81 to both sides of the equation: \(x^{4}=81\).
03

Simplify the equation and find the solution(s)

To find the solutions of the equation \(x^{4} = 81\), we will take the fourth root of both sides: \(x = \pm\sqrt[4]{81}\). Using a calculator, we find that the fourth root of 81 is approximately: \(\sqrt[4]{81} \approx 3.0000\). Thus, we have two solutions for x: \(x \approx 3.0000\) and \(x \approx -3.0000\). So, the solutions for the given equation, rounded to four significant digits, are: \(x \approx 3.0000\) and \(x \approx -3.0000\).

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