Problem 117 Solve each equation, rounding yo... [FREE SOLUTION]

Chapter 0: Problem 117

Solve each equation, rounding your answer to four significant digits where necessary. $$ 1-\frac{1}{x^{2}}=0 $$

Short Answer

Expert verified

The solution to the equation $1-\frac{1}{x^{2}}=0$ is $x=1, -1$.

Step by step solution

Identify the equation#gtag_content#The given equation is: \[ 1-\frac{1}{x^{2}}=0 \]

Step 2: Add the fraction to both sides of the equation#gtag_content#Adding the fraction $\frac{1}{x^{2}}$ to both sides, we get: \[ 1 = \frac{1}{x^{2}} \]

Find the reciprocal of both sides of the equation#gtag_content#To solve for $x^2$, take the reciprocal of both sides: \[ x^{2} = \frac{1}{1} \]

Step 4: Simplify the equation#gtag_content#The simplified equation is: \[ x^{2} = 1 \]

Solve for x#gtag_content#To find the values of x, take the square root of both sides: \[ x = \pm \sqrt{1} \]

Step 6: Simplify the values#gtag_content#Since the square root of 1 is simply 1: \[ x = \pm 1 \] The two possible values of x are 1 and -1. Since no rounding is necessary, our final answer is: \[ x = 1, -1 \]

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91影视

Solve each equation, rounding your answer to four significant digits where necessary. $$ 1-\frac{1}{x^{2}}=0 $$

Short Answer

Step by step solution

Identify the equation#gtag_content#The given equation is: \[ 1-\frac{1}{x^{2}}=0 \]

Find the reciprocal of both sides of the equation#gtag_content#To solve for \(x^2\), take the reciprocal of both sides: \[ x^{2} = \frac{1}{1} \]

Solve for x#gtag_content#To find the values of x, take the square root of both sides: \[ x = \pm \sqrt{1} \]

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