Solve the equation. Check all proposed solutions. Show work in solving and in checking.
sqrt3-x=x-1
Here is the problem
sqrt3-x=x-1
Is the left side of the equation
sqrt(3-x) or (sqrt3) - x?
If you meant
sqrt(3-x) = x-1, then, from squaring both sides,
3-x = x^2 -2x +1
x^2 -x -2 = 0
(x-2)(x+1) = 0
x = 2 or -1
The second value (-1) works if negative value of the square root are allowed.
The problem has no parenthases. it is as follows sqrt3-x=x-1. So do we put parenthases automatically around the (3-x)? Thanks!
Check out the thread by Kim with many posts.
That thread is very similar: symbols such as square roots or division with a numerator over a denominator separated with a bar have assumed parentheses. When writing in a single line, those parentheses must be included for clarity.
To solve the equation √3 - x = x - 1, we will follow these steps:
Step 1: Simplify the equation.
Step 2: Isolate the square root term.
Step 3: Square both sides of the equation.
Step 4: Solve for x.
Step 5: Check proposed solutions.
Let's begin:
Step 1: Simplify the equation.
We don't have any like terms to combine, so we move on to the next step.
Step 2: Isolate the square root term.
Move the x term to the left side of the equation and the constant term to the right side:
√3 - x + x = x - x - 1 + √3
√3 = -1 + √3
Step 3: Square both sides of the equation.
To eliminate the square root on the left side of the equation, we square both sides:
(√3)^2 = (-1 + √3)^2
3 = (-1)^2 + 2*(-1)*√3 + (√3)^2
3 = 1 - 2√3 + 3
Step 4: Solve for x.
Simplify the equation:
3 = 4 - 2√3
Rearrange the terms:
-2√3 = 1
Divide both sides by -2:
√3 = -1/2
At this point, we have an error since we cannot have a negative value on the left side of the equation when dealing with real numbers. Therefore, there is no solution to this equation.
Step 5: Check proposed solutions.
Since we didn't find any proposed solutions, we don't have to check them.
In conclusion, the equation √3 - x = x - 1 has no solutions.