Questions: x^-2-4 x^-1+3=0 x=-3, 3

x^-2-4 x^-1+3=0 x=-3, 3
Transcript text: \[ \begin{array}{l} x^{-2}-4 x^{-1}+3=0 \\ x=-3 \quad \times, 3 \quad \times \end{array} \]
failed

Solution

failed
failed

Solve the equation \( x^{-2} - 4x^{-1} + 3 = 0 \).

Rewrite the equation in terms of \( y \).

Let \( y = x^{-1} \). Then, the equation becomes \( y^2 - 4y + 3 = 0 \).

Factor the quadratic equation.

The factorized form of the polynomial is \( (y - 3)(y - 1) = 0 \).

Solve for \( y \).

Setting each factor to zero gives \( y = 3 \) and \( y = 1 \).

Convert back to \( x \).

Using \( y = x^{-1} \), we find \( x = \frac{1}{3} \) and \( x = 1 \).

The solutions for \( x \) are \( \boxed{x = 1} \) and \( \boxed{x = \frac{1}{3}} \).

The solutions for the equation are \( \boxed{x = 1} \) and \( \boxed{x = \frac{1}{3}} \).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
5. In the space provided, label each function as even, odd, or neither. a) f(x) = x^4 - 5 b) f(x) = x^4 + x c) f(x) = -2x^3 7. Sketch a graph of the following functions a) f(x) = x - 2 b) f(x) = sqrt(x) + 1 c) f(x) = (x + 2)^2 - 3 d) f(x) = -x 8. Write the function whose graph is the graph of f(x) = sqrt(x), but is a) shifted left 3 b) shifted down 5 c) reflected over the y-axis d) shifted right 1
failedAnswered
Suppose that at Northside High, the number of hours per week that seniors spend on homework is approximately Normally distributed with a mean of 18.6 hours and a standard deviation of 6 hours. For simple random samples of size n=36 from this population, you determine that the sampling distribution of the sampling distribution of the sample mean is approximately normal with a mean of 18.6 hours and a standard deviation of 6/sqrt(36)=1 hour. If you discover that Northside High has only 200 seniors, which of the following would no longer be correct? - the mean and the standard deviation - the standard deviation and the shape of the distribution - All three would be incorrect. - only the standard deviation - only the shape of the distribution
failedAnswered
What type of reaction is this? LiClO3 → LiCl + O2 A. decomposition B. neutralization C. single displacement D. combustion E. double displacement
failedAnswered
The table summarizes results from 981 pedestrian deaths that were caused by automobile accidents. Driver Intoxicated? Pedestrian Intoxicated? Yes No --------- Yes No 231 67 If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol. prob = 0.4
failedAnswered
The mean value of land and buildings per acre from a sample of farms is 1700, with a standard deviation of 300. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? 1355 2449 1308 563 2069 1804 E. 2449 F. 1308 Which of the farms are very unusual (more than three standard deviations from the mean)? Select all that apply. A. 1804 B. 1308 C. 2449 D. 563 E. 2069 F. 1355 G. None of the data values are very unusual.