Respuesta :

smayra1191

Answer:

The smallest number is x = -2

for which this statement holds !!

Step-by-step explanation:

Let as assume the number be x

then the number is one less than twice its reciprocal i.e,

[tex] x = \frac{2}{x} - 1[/tex]

[ For solution refer to the attached file ]

  • Method used to solve quadratic equation is Splitting the middle term !!

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The required smallest number which is one less than twice its reciprocal is -2.

Given that,
To determine the smallest number which is one less than twice it's reciprocal

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements.

Let the number be x,
the number which is one less than twice its reciprocal
x = 2/x - 1
x² = 2 - x
x² + x - 2 = 0
x² + 2x - x - 2 = 0
x (x + 2) - 1 (x + 2) = 0
(x - 1) . (x + 2) = 0
x - 1 = 0   ;    x + 2 = 0
x = 1        ;     x = -2
-2 is the smallest number among the two,

Thus, the required smallest number which is one less than twice its reciprocal is -2.

Learn more about arithmetic here:

brainly.com/question/14753192

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