For this case we have:
[tex]x[/tex]: Let the variable representing the first odd number
[tex]x + 2[/tex]: Let the variable representing the consecutive odd number at x.
According to the statement we have:
[tex]x (x + 2) = 63\\x ^ 2 + 2x = 63\\x ^ 2 + 2x-63 = 0[/tex]
We found the solution by factoring:
We look for two numbers that, when multiplied, result in -63 and when added, result in 2. These numbers are +9 and -7.
[tex]9-7 = 2\\9 * (-7) = -63[/tex]
Thus, we have:
[tex](x + 9) (x-7) = 0[/tex]
Therefore the solutions are:
[tex]x_ {1} = - 9\\x_ {2} = 7[/tex]
We choose the positive value, so we have:
[tex]x = 7\\x + 2 = 7 + 2 = 9[/tex]
Answer:
The largest number is 9
