Answer :
The two positive whole numbers that satisfy the given conditions are 7 and 2.
To find two positive whole numbers that differ by 5 and have a sum of squares equal to 193, we can approach this problem systematically.
Let's assume the smaller number is "x." According to the conditions, the other number is "x + 5."
We can set up the equation based on the sum of their squares:
[tex]x^2[/tex] + [tex](x + 5)^2[/tex] =193
Solving this quadratic equation yields two possible solutions: x = 2 and x = 7.
Therefore, the two positive whole numbers that satisfy the conditions are 2 and 7. Their difference is indeed 5, and the sum of their squares is 193.
To solve this problem, we start by defining the two positive whole numbers. Let x represent the smaller number, and since the numbers differ by 5, the other number can be expressed asx + 5. This gives us our first step.
In the second step, we set up an equation using the sum of their squares, as provided in the question: [tex]x^2[/tex] + [tex](x + 5)^2[/tex] = 193. By expanding the equation and simplifying, we arrive at a quadratic equation: 2[tex]x^2[/tex] + 10x - 168 = 0. We then solve this quadratic equation to find the possible values of x, which are 2 and 7.
Finally, moving on to step three, we confirm that the pair of numbers 2 and 7 indeed satisfies the given conditions. The difference between these two numbers is 5, which aligns with the problem statement. Additionally, when we calculate the sum of their squares [tex]2^2[/tex] + [tex]7^2[/tex] = 4 + 49 = 53 , it is equal to 193, just as required.
In conclusion, by systematically approaching the problem and solving the relevant equations, we have identified that the positive whole numbers 2 and 7 satisfy the given conditions.
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