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[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

let one of the integers be x,

other one = 2x - 2

now, according to question :

  • [tex] {x}^{2} + (2x - 2) {}^{2} = 628[/tex]

  • [tex] {x}^{2} + 4 {x}^{2} + 4 - 8 x = 628[/tex]

  • [tex]5 {x}^{2} - 8x = 628 - 4[/tex]

  • [tex]5 {x}^{2} - 8x = 624[/tex]

  • [tex]5 {x}^{2} - 8x - 624 = 0[/tex]

  • [tex]5 {x}^{2} - 60 x+ 52 x- 624 = 0[/tex]

  • [tex]5x(x - 12) + 52(x - 12) = 0[/tex]

  • [tex](5x + 52)(x - 12) = 0[/tex]

now, since the Integers are positive so the value obtained from (5x + 52) = 0 can't hold true.

so, x - 12 = 0

  • [tex]x = 12[/tex]

the first number is :

  • [tex]x = 12[/tex]

second number is :

  • [tex]2x - 2[/tex]

  • [tex](2 \times 12) - 2[/tex]

  • [tex]24 - 2[/tex]

  • [tex]22[/tex]

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