Question

√(m-n)^2-√9m^2 если m<0

Answer 1

$m$

Answer 2

Let's simplify the expression step by step:

Given: √(m-n)^2 - √9m^2

Since m < 0, we can use the property that √(x^2) = |x|, where |x| is the absolute value of x.

1. √(m-n)^2 = |m-n|

2. √9m^2 = √(9 * m^2) = |3m|

Therefore, the expression becomes:

|m-n| - |3m|

We need to consider two cases for the absolute values:

Case 1: (m-n) ≥ 0 and 3m ≥ 0 In this case, both |m-n| and |3m| will be without the absolute value signs.

So, the expression becomes: (m-n) - (3m) = m - n - 3m = -2m - n.

Case 2: (m-n) < 0 and 3m < 0 In this case, both |m-n| and |3m| will have a negative sign.

So, the expression becomes: -(m-n) - (-3m) = -m + n + 3m = 2m + n.

In summary:

• If m < 0, the expression simplifies to: -2m - n when (m-n) ≥ 0 and 3m ≥ 0 2m + n when (m-n) < 0 and 3m < 0

Keep in mind that the exact value of the expression will depend on the specific values of 'm' and 'n.'