what is the positive solution of the equation x^2 - 3x = 1? solve by using a table or by graphing. if necessary, round your answer to the nearest hundredth.
See the graph at
http://www.wolframalpha.com/input/?i=solve+x^2+-+3x+%3D+1
To solve the equation x^2 - 3x = 1, we can solve it by graphing or using a table.
Let's solve it using a table:
Step 1: Create a table and choose some values for x:
x | x^2 - 3x
_________|___________
0 | -1
1 | -2
2 | -1
3 | 2
4 | 7
Step 2: Calculate the corresponding values of x^2 - 3x in the table.
Step 3: See if any of the calculated values are equal to 1.
From the table, we can see that the value of x^2 - 3x equals 1 when x is approximately 2.
Therefore, the positive solution of the equation x^2 - 3x = 1 is x ≈ 2 (rounded to the nearest hundredth).
To find the positive solution of the equation x^2 - 3x = 1, we can solve it by using a table or by graphing.
Method 1: Using a table
1. Create a table with two columns, labeled "x" and "y."
2. Choose a range of x-values that you think might include the solution. For example, let's choose x-values from -10 to 10.
3. Plug in each x-value into the equation x^2 - 3x = 1 to find the corresponding y-value.
- For example, when x = -10, y = (-10)^2 - 3(-10) = 100 + 30 = 130.
4. Record the x and y values in the table.
5. Look for the x-value that corresponds to the y-value of 1 (as given in the equation). This will give you the positive solution.
Method 2: Graphing
1. Plot the graph of the equation y = x^2 - 3x - 1. You can do this on graph paper or using graphing software.
2. Determine the x-coordinate(s) where the graph intersects the y = 1 line. This will give you the solution(s) to the equation.
3. Identify the x-value(s) on the graph that correspond to the points of intersection with y = 1. These will be the positive solution(s) you are looking for.
4. If necessary, round the positive solution(s) to the nearest hundredth, as specified in the question.
By using either method, you should be able to find the positive solution of the equation x^2 - 3x = 1.