Answer :

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

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:

  1. Let x be the smaller number. Then the larger number is x + 5.
  2. 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:

  1. x^2 + (x + 5)(x + 5) = 193
  2. x^2 + x^2 + 10x + 25 = 193
  3. 2x^2 + 10x + 25 = 193
  4. 2x^2 + 10x - 168 = 0

Using the quadratic formula, we can solve for x:

  1. x = (-10 ± √(10^2 - 4*2*-168)) / (2*2)
  2. x = (-10 ± 62) / 4
  3. 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:

https://brainly.com/question/18322830

#SPJ3

Other Questions