Answer:
10 and 19
Step-by-step explanation:
- In Algebra, an even number = 2x, because anything multiplied by 2 is even.
- There are two numbers in the question, I'll define the first one as 2x
- the other number is 1 less than twice of the first, so I'm going to define it in algebra as 2(2x) - 1, which is just 4x - 1
- the square of the first is [tex]4x^2[/tex]
- the square of the second is [tex]16x^2-8x+1[/tex]
- add them together: [tex]20x^2-8x+1[/tex]
- this equation = 461, so [tex]20x^2-8x+1 = 461[/tex]
- simplify to [tex]20x^2-8x-460 = 0[/tex]
- I wont explain how to solve this here, since it is very complicated, if you don't know search up solving quadratics.
- the solutions are 5 or -4.6, it cannot be -4.6 since the question says positive, so the solution for x = 5
- substitute x into our equations for the two numbers in steps 1 and 2
- the first number = 10, the second = 19
