Respuesta :

sqdancefan

Answer:

  1

Step-by-step explanation:

Let x represent the number. The given relation is ...

  x² +(x+3)² = 17

  2x² +6x +9 = 17 . . . . simplify

  x² +3x -4 = 0 . . . . . . subtract 17 and divide by 2

  (x +4)(x -1) = 0 . . . . . factor

The solutions make these factors zero: -4 and +1. The positive solution is 1.

The number is 1.

Lanuel

The number is equal to 1.

  • Let the positive number be p.

In this exercise, you're required to write an algebraic expression and solve for the unknown variable or number.

Translating the word problem into an algebraic expression, we have;

[tex]p^{2} + (p + 3)^2 = 17\\\\p^{2} + p^{2} + 3p + 3p + 9 = 17\\\\2p^{2} + 6p + 9 = 17\\\\2p^{2} + 6p = 17 - 9\\\\2p^{2} + 6p = 8[/tex]

Dividing all through by 2, we have;

[tex]p^{2} + 3p = 4\\\\p^{2} + 3p - 4 = 0[/tex]

Solving the quadratic equation by factorization, we have;

[tex]p^{2} + 4p - p - 4 = 0\\\\p(p + 4) - 1(p + 4) = 0\\\\(p + 4)(p - 1) = 0[/tex]

Since the number is a positive number, then p = 1

Therefore, the number is equal to 1.

Find more information: https://brainly.com/question/3158507

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