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Effectus [21]
2 years ago
10

One positive integer is 2 less than twice another. The sum of their squares is 628. Find the integers.

Mathematics
1 answer:
lana66690 [7]2 years ago
5 0

▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪

let one of the integers be x,

other one = 2x - 2

now, according to question :

  • {x}^{2}  + (2x - 2) {}^{2}  = 628

  • {x}^{2}  + 4 {x}^{2}  + 4 - 8  x = 628

  • 5 {x}^{2}  - 8x = 628 - 4

  • 5 {x}^{2}  - 8x = 624

  • 5 {x}^{2}  - 8x - 624  = 0

  • 5 {x}^{2}  - 60 x+ 52 x- 624 = 0

  • 5x(x - 12) + 52(x - 12) = 0

  • (5x + 52)(x - 12) = 0

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

so, x - 12 = 0

  • x = 12

the first number is :

  • x = 12

second number is :

  • 2x - 2

  • (2 \times 12) - 2

  • 24 - 2

  • 22
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