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Answer :
Final answer:
To find the numbers, we set up two equations and solve for x using the quadratic formula.
Explanation:
To solve this problem, we can set up two equations:
- Let x be the smaller number. Then the larger number is x + 5.
- The sum of their squares is 193, so we have x^2 + (x + 5)^2 = 193.
We can solve this equation by expanding and simplifying it:
- x^2 + (x + 5)(x + 5) = 193
- x^2 + x^2 + 10x + 25 = 193
- 2x^2 + 10x + 25 = 193
- 2x^2 + 10x - 168 = 0
Using the quadratic formula, we can solve for x:
- x = (-10 ± √(10^2 - 4*2*-168)) / (2*2)
- x = (-10 ± 62) / 4
- x = (-10 + 62) / 4 = 13
Therefore, the smaller number is 13 and the larger number is 13 + 5 = 18.
Learn more about solving equations here:
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Answer:
Let one number be x and the other be (x-5)
Step-by-step explanation:
x^2+(x-5)^2=193
x^2+x^2-10x+25=193
2x^2-10x+25=193
Subtract 193 from both sides of the equation.
2x^2-10x-168=0
x=12 or x=-7
x-5=7 or x-5=-12
