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Answer :
Final answer:
The two solutions represent two numbers that differ by 5 and whose squares sum to 157. If one number is x, then the other number is (x-5). The zero product property is used to solve the equation.
Explanation:
In the given equation x² + (x - 5)² = 157, the two solutions that you get by employing the zero product property will represent two numbers that differ by 5 and whose squares sum to 157. Therefore, if you let one number be \(x\), then the other number will be \(x-5\). These two numbers meet the conditions specified in the problem: they have a difference of 5, and if you square each number and add these squares together, you get 157. The zero-product property is used in the process of finding these solutions.
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