Problem

If the mean of the data set \(x^2 - 7x + 10\), \(x^2 - 5x + 6\), and \(x^2 - 3x + 2\) is \(x^2 - 5x + 6\), what is the value of \(x\)?

Solution

Step 1 :Step 1: Set up the equation for the mean of the data set. The mean is the sum of the values divided by the number of values. So we have \(\frac{x^2 - 7x + 10 + x^2 - 5x + 6 + x^2 - 3x + 2}{3} = x^2 - 5x + 6\).

Step 2 :Step 2: Simplify the equation. Combine like terms to get \(\frac{3x^2 - 15x + 18}{3} = x^2 - 5x + 6\).

Step 3 :Step 3: Multiply both sides by 3 to get rid of the fraction. This gives us \(3x^2 - 15x + 18 = 3x^2 - 15x + 18\).

Step 4 :Step 4: Subtract \(3x^2 - 15x + 18\) from both sides. This gives us \(0 = 0\).

Step 5 :Step 5: Since the equation is always true, there are infinite solutions for \(x\).

From Solvely APP
Source: https://solvelyapp.com/problems/rl2IW2Vusz/

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