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Complete the table and find the rule: Input [x]: 1, 2, 4, (missing value) Output [y]: 1, 4, 9, 25

Mathematics

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Answer

To complete the table and find the rule, we need to identify the relationship between the input $[x]$ and the output $[y]$.

The given values are:
Input [x][x]: 1, 2, 4, (missing value)
Output [y][y]: 1, 4, 9, 25

Step 1: Analyze the outputs.
Notice that the outputs are perfect squares:
1=121 = 1^2
4=224 = 2^2
9=329 = 3^2
25=5225 = 5^2

Let kk be the base of the square, so y=k2y = k^2. We can list the corresponding kk values:
For $x=1

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