Solve Floor Equation 7: x^2=2x-1

  • MHB
  • Thread starter solakis1
  • Start date
In summary, a floor equation is an equation where the variable represents an integer and the solution is rounded down to the nearest whole number. To solve a floor equation, the variable must be isolated and the floor must be taken of both sides of the equation. The "x^2=2x-1" means that the variable is being squared and the result is equal to 2 times the variable minus 1. The purpose of rounding down in a floor equation is to ensure that the solution is a counting number. There are specific steps to follow when solving a floor equation, including isolating the variable, taking the floor, and checking for a counting number solution. It is important to follow these steps correctly for an accurate solution.
  • #1
solakis1
422
0
Solve the following equation:

$[x]^2=[2x]-1$ where [x] is the floor value of the x real No

[sp] hint : start by puting x=n+b where n is an integer and $0\leq b<1$[/sp]
 
Mathematics news on Phys.org
  • #2
Let x = n + r where n is the integer part and r is the fractional part

we have

$\lfloor x \rfloor ^2 = 2(x+r) - 1$

so $n^2 = 2n -1$ when $ r\lt \frac{1}{2}$ or $n^2 = 2n$ and $ \frac{1}{2} \le r \lt 1$

$n^2 = 2n -1$ when $ r\lt \frac{1}{2}$

gives $n^2 - 2n + 1 = 0$ or $(n-1)^2 =0 $ or n= 1 giving $ 1 \le x \lt 1.5$

$n^2 = 2n$ and $\frac{1}{2} \le r \lt 1$

gives n = 0 or 2 giving $ .5 \le x \lt 1$ or giving $ 2.5 \le x \lt 3$

combining them we have $ .5 \le x \lt 1. 5 $ or $ 2.5 \le x \lt 3$
 
  • #3
ok kaliprasad that's it good work
 

Related to Solve Floor Equation 7: x^2=2x-1

1. What is a floor equation?

A floor equation is an equation that involves finding the value of a variable that satisfies a given condition. In this case, we are solving for the value of x that makes the equation x^2 = 2x-1 true.

2. How do you solve a floor equation?

To solve a floor equation, we need to isolate the variable on one side of the equation by using algebraic operations such as addition, subtraction, multiplication, and division. The goal is to get the variable by itself on one side and the constant on the other side.

3. What is the process for solving the equation 7: x^2=2x-1?

To solve this equation, we first need to subtract 2x from both sides to get x^2-2x = -1. Then, we can add 1 to both sides to get x^2-2x+1 = 0. This can be factored into (x-1)^2 = 0. Therefore, the solution is x=1.

4. Can a floor equation have multiple solutions?

Yes, a floor equation can have multiple solutions. In this case, the equation x^2 = 2x-1 has two solutions, x=1 and x=0. However, not all floor equations will have multiple solutions.

5. How do you know if your solution is correct for a floor equation?

To check if your solution is correct for a floor equation, you can substitute the value of x into the original equation and see if it satisfies the equation. In this case, we can substitute x=1 and x=0 into x^2 = 2x-1 and see that both values satisfy the equation.

Similar threads

  • General Math
Replies
3
Views
916
  • General Math
Replies
14
Views
1K
Replies
4
Views
910
  • General Math
Replies
7
Views
1K
Replies
6
Views
931
Replies
9
Views
2K
Replies
1
Views
664
  • General Math
Replies
4
Views
960
Replies
12
Views
994
  • General Math
Replies
1
Views
702
Back
Top