Solve the equation. Check all proposed solutions. Show work in solving and in checking.
Root3-x = x-1
sqrt(3-x) = x-1.
Start by squaring both sides.
3 - x = x^2 - 2x + 1
0 = x^2 - x - 2
Factor the equation:
0 = (x-2)(x+1)
So x = 2 or x = 1
you made a mistake it is x=2 or x=1 its x=2 or x=-1
I am still confused. Can someone please explain further and break this problem down cause I have 5 more like this one to do. Thank you!
from Marth's last line
So x = 2 or x = 1 ...
that should have said
So x = 2 or x = -1
Since he squared both sides, all answers must be verified.
if x=2
LS = √(3-2) = √1 = 1
RS = 2-1 = 1 OK
if x = -1
LS = √(3+1) = √4 = 2
RS = -1 - 1 = -2
so LS is not equal to RS
so the only solution is x = 2
2 or 1 or
2 or -1?
annaiiz ceballos said
it is x=2 or x=1 its x=2 or x=-1
To solve the equation √3 - x = x - 1, we'll follow the steps below:
Step 1: Move the x term to one side of the equation.
√3 - x = x - 1
√3 + 1 = x + x
√3 + 1 = 2x
Step 2: Simplify the equation.
√3 + 1 = 2x
√3 + 1 = 2x
√3 + 1 - 1 = 2x - 1
√3 = 2x - 1
Step 3: Divide by 2 to isolate x.
√3 = 2x - 1
√3 / 2 = (2x - 1) / 2
√3 / 2 = x - 1/2
Step 4: Add 1/2 to both sides of the equation.
√3 / 2 + 1/2 = x - 1/2 + 1/2
√3 / 2 + 1/2 = x
Step 5: Simplify both sides of the equation.
(√3 + 1) / 2 = x
So the solution to the equation √3 - x = x - 1 is x = (√3 + 1) / 2.
To check the solution, substitute the value of x back into the original equation (√3 - x = x - 1) and see if both sides are equal.
√3 - x = x - 1
√3 - [ (√3 + 1) / 2 ] = [ (√3 + 1) / 2 ] - 1
Simplify the equation:
√3 - (√3 + 1) / 2 = (√3 + 1) / 2 - 1
To confirm the solution, substitute √3 = 1.732, and calculate both sides of the equation. If both sides are equal, then the solution is correct.