Question

Раскрыть модуль /x^2+х+0.25/

Answer 1

/x^2+х+0.25/=/x^2+2*0,5*х+0.5^2/=|(x+0.5)^2|=x+0.5

неотрицательное раскрываем без смены знака

Answer 2

To simplify the expression |x^2 + x + 0.25|, we need to consider two cases based on the value of the expression inside the absolute value.

Case 1: x^2 + x + 0.25 ≥ 0 In this case, the expression inside the absolute value is non-negative. So, we can remove the absolute value without changing the value of the expression.

|x^2 + x + 0.25| = x^2 + x + 0.25

Case 2: x^2 + x + 0.25 < 0 In this case, the expression inside the absolute value is negative. To keep the absolute value positive, we need to negate the expression inside the absolute value.

|x^2 + x + 0.25| = -(x^2 + x + 0.25)

Combining both cases, we get:

|x^2 + x + 0.25| = { x^2 + x + 0.25, if x^2 + x + 0.25 ≥ 0, -(x^2 + x + 0.25), if x^2 + x + 0.25 < 0 }

Now, we can try to factor the expression x^2 + x + 0.25 to understand when it's positive or negative.

x^2 + x + 0.25 = (x + 0.5)^2

Since it's a perfect square, it is always non-negative, and thus, the absolute value will always be the expression itself:

|x^2 + x + 0.25| = x^2 + x + 0.25

So, the simplified expression for |x^2 + x + 0.25| is just x^2 + x + 0.25.