Can you help me with this math question?

Question

√(2-x) = 2-x

Is the answer you get supposed to take the place of x. When I do these, sometimes the answer does not work for x. Am I doing something wrong.

Answer 1

√(2-x) = 2-x
Square both sides
2-x = 4 -4x +x^2
x^2-3x+2=0
(x-1)(x-2) = 0
x = 1, 2

Answer 2

√(2 - x) = 2 - x. Square both sides.
√(2 - x)² = (2 - x)². Simplify.
|2 - x| = 4 - 4x + x². Solving the absolute value yields two possibilities:
(2 - x) = 4 - 4x + x² or -(2 - x) = 4 - 4x + x².
On the left,
2 - x = 4 - 4x + x².
x² - 3x + 2 = 0.
(x - 2)(x - 1) = 0.
x = 2 or x = 1.
On the right,
-(2 - x) = 4 - 4x + x².
-2 + x = 4 - 4x + x².
x² - 5x + 6 = 0.
(x - 3)(x - 2) = 0.
x = 3 or x = 2.

When solving radical equations, always check for extraneous solutions that may come about from squaring.
x = 1 is good. √(2 - 1) = 2 - 1... √1 = 1.
x = 2 is good. √(2 - 2) = 2 - 2... √0 = 0.
x = 3 is not a valid solution. √(2 - 3) = 2 - 3... √-1 = -1.

The valid solutions are x = 1 or x = 2.

Answer 3

Hi,

For this question, it looks like you have the following:

Sqr. root(2 - x) = 2 - x

Now, you should square both sides to get rid of the square root:

2 - x = (2-x)(2-x)

Now notice that there's a common factor on both sides of the equation of 2-x. Divide both sides by 2-x to get the following:

2 - x = 1

Now, subtract 2 from both sides of the equation:

- x = - 1

Divide both sides by negative 1 and get: x = 1

I hope that helps you out! Please let me know if you have any other questions!

Sincerely,

Andrew

Answer 4

I'll show you step by step.

2-x=(2-x)^2
2-x=4- 4x +x^2
x^2 -3x +2 =0
(x-1)(x-2)=0
x=1, x=2

Now put them back into the equation to check your work.

2-1=(2-1)^2
1=1
that works

2-2=(2-2)^2
0=0
that also works

The answer is x=1,,2

Answer 5

square both sides:
(2-x)=(2-x)^2
2-x =4 -4x + x^2
combine like terms
0=2-3x+x^2
factor
0=(2-x)(1-x)
x=2 and x=1

these both satisfy the equation

Answer 6

do get rid of the sqr. you have to sq. both sides.

[ √(2-x) ]^2 = [2-x]^2
2-x = 4 - 4x + x^2
0 = 2 - 3x + x^2
factor and solve for x

Answer 7

by squaring, 2-x=(2-x)(2-x)
therefore taking (2-x) on the other side and taking it common,
(2-x)(2-x-1)=0
(2-x)(1-x)=0
that implies (2-x)=0 or (1-x)=0
that imples x=2 or x=1 which are the answers

Answer 8

let z = 2-x
sqr(z) = z
z^2 = z
z^2-z = 0
z(z-1) = 0
z = 0 or z = 1
x = 2 or x = 1

Answer 9

:D