Answer:
Step-by-step explanation:
Given 
, start by squaring both sides to work towards isolating 
:
Recall 
and 
:
Isolate the radical:
Square both sides:
Expand using FOIL and 
:
Move everything to one side to get a quadratic:
Solving using the quadratic formula:
A quadratic in 
has real solutions 
. In 
, assign values:
Solving yields:
Only works when plugged in the original equation. Therefore, 
is extraneous and the only solution is 
Answer:
Step-by-step explanation:
Answer:
0.5<2-√2<0.6
Step-by-step explanation:
The original inequality states that 1.4<√2<1.5
For the second inequality, you can think of 2-√2 as 2+(-√2).
Because of the "properties of inequalities", we know that when a positive inequality is being turned into a negative, the numbers need to swap and become negative. So, the original inequality becomes -1.5<-√2<-1.4. (Notice how the √2 becomes negative, too). This makes sense because -1.5 is less than -1.4.
Using our new inequality, we can solve the problem. Instead of 2+(-√2), we are going to switch "-√2" with both possibilities of -1.5 and -1.6. For -1.5, we would get 2+(-1.5), or 0.5. For -1.4, we would get 2+(-1.4), or 0.6.
Now, we insert the new numbers into the equation _<2-√2<_. The 0.5 would take the original equation's "1.4" place, and 0.6 would take 1.5's. In the end, you'd get 0.5<2-√2<0.6. All possible values of 2-√2 would be between 0.5 and 0.6.
Hope this helped!
3.305
+1.7
5.005
Line up the decimal points and add like you usually would add.
5.005 is the answer.
Your answer is the first one q
