Good morning ☕️
Answer:
<h2>x ≥ 2</h2>
Step-by-step explanation:
our expression is defined when x ≥ 1 ,
because , when x ≥ 1
x - 1 ≥ 0
x + 2√(x - 1) ≥ 0
x - 2√(x - 1) ≥ 0
![Calculations:\\\\(\sqrt{x+2\sqrt{x-1} } -\sqrt{x-2\sqrt{x-1} } )^{2} =2^2\\\\then\\\\(x+2\sqrt{x-1} ) +(x-2\sqrt{x-1} ) -2(\sqrt{x+2\sqrt{x-1} })(\sqrt{x-2\sqrt{x-1} } )=4\\\\then\\\\2x - 2\sqrt{(x+2\sqrt{x-1} )(x-2\sqrt{x-1} ) }=4 \\\\then\\\\2x -2\sqrt{(x-2)^2} = 4\\\\then\\\\2x -2|x - 2| =4\\\\then\\\\x - |x-2|=2\\\\now,\\\\case1 : (x\geq2)\\ x - |x-2|=2 \\means \\x-(x-2)=2\\means\\2=2\\\\case2: (1 \leq x \leq2)\\x - |x-2|=2 \\means \\x-(2-x)=2\\means\\2x-2=2\\means\\x=2](https://tex.z-dn.net/?f=Calculations%3A%5C%5C%5C%5C%28%5Csqrt%7Bx%2B2%5Csqrt%7Bx-1%7D%20%7D%20-%5Csqrt%7Bx-2%5Csqrt%7Bx-1%7D%20%7D%20%29%5E%7B2%7D%20%3D2%5E2%5C%5C%5C%5Cthen%5C%5C%5C%5C%28x%2B2%5Csqrt%7Bx-1%7D%20%29%20%2B%28x-2%5Csqrt%7Bx-1%7D%20%29%20-2%28%5Csqrt%7Bx%2B2%5Csqrt%7Bx-1%7D%20%7D%29%28%5Csqrt%7Bx-2%5Csqrt%7Bx-1%7D%20%7D%20%29%3D4%5C%5C%5C%5Cthen%5C%5C%5C%5C2x%20-%202%5Csqrt%7B%28x%2B2%5Csqrt%7Bx-1%7D%20%29%28x-2%5Csqrt%7Bx-1%7D%20%29%20%7D%3D4%20%5C%5C%5C%5Cthen%5C%5C%5C%5C2x%20-2%5Csqrt%7B%28x-2%29%5E2%7D%20%3D%204%5C%5C%5C%5Cthen%5C%5C%5C%5C2x%20-2%7Cx%20-%202%7C%20%3D4%5C%5C%5C%5Cthen%5C%5C%5C%5Cx%20-%20%7Cx-2%7C%3D2%5C%5C%5C%5Cnow%2C%5C%5C%5C%5Ccase1%20%3A%20%28x%5Cgeq2%29%5C%5C%20x%20-%20%7Cx-2%7C%3D2%20%5C%5Cmeans%20%5C%5Cx-%28x-2%29%3D2%5C%5Cmeans%5C%5C2%3D2%5C%5C%5C%5Ccase2%3A%20%281%20%5Cleq%20x%20%5Cleq2%29%5C%5Cx%20-%20%7Cx-2%7C%3D2%20%5C%5Cmeans%20%5C%5Cx-%282-x%29%3D2%5C%5Cmeans%5C%5C2x-2%3D2%5C%5Cmeans%5C%5Cx%3D2)
According to case 1 and 2 the solution set for this equality is {x real number where x ≥ 2 }.
The statement is an equation which is written in text form or in words. when we write it as an equation it will be:
squares of w and x is equal to w² and x² so, their sum means they are going to add.
3 + (w² + x²) = 32
three plus the sum of w² and x² is 32.
when we describe or write quantity with an equal sign it makes an equation.
2c + 5c - 25 = 10
7c = 35
c = 5
the answer is c= 5
Answer:
1/4 of the pizza.
Step-by-step explanation:
Since there are 2 people, you would want to divide 2/4 by 2. 2/4*1/2 = 1/4, so your answer is 1/4.
Answer:
(0, - 3.5 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[
(x₁ + x₂ ),
(y₁ + y₂ ) ]
Here (x₁, y₁ ) = A(- 5, - 4) and (x₂, y₂ ) = B(5, - 3)
midpoint = [
(- 5 + 5),
(- 4 - 3 ) ] = (
(0),
(- 7) ) = (0, - 3.5 )