Respuesta :
Building an equation and solving it, it is found that the number is 4.
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- The number is unknown, so it is called x.
- The square of 1 is [tex]1^2 = 1[/tex], the square of 2 is [tex]2^2 = 4[/tex], thus the square of the number x is [tex]x^2[/tex].
- 8 times the number is 8x.
- 16 less than 8 times the number is 8x - 16.
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The equality is:
[tex]x^2 = 8x - 16[/tex]
[tex]x^2 - 8x + 16 = 0[/tex]
Applying the perfect square binomial:
[tex](x - 4)^2 = 0[/tex]
[tex]\sqrt{(x - 4)^2} = \sqrt{0}[/tex]
[tex]x - 4 = 0[/tex]
[tex]x = 4[/tex]
The number is 4.
A similar problem is given at https://brainly.com/question/20742606
