Addition Is The Same As Multiplication?
Algebra
Level
1
Which positive number has the following property:
Adding it to itself gives the same result as squaring it.
The answer is 2.
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Let X denote this number.
If a number adds itself, it means that X + X = 2 X .
If we square a number, it means that X 2 .
Since we told that the adding itself equals squaring itself, then 2 X = X 2 .
Rearrange all the terms to one side of the equation and factoring it gives 2 X − X 2 = 0 or X ( 2 − X ) = 0 .
By zero product property , X = 0 or X = 2 only.
But since we're looking for positive number only, then X = 2 only. So our answer is 2 .