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3 years ago

What is the solution of x equals 2 + sqrt x - 2

Mathematics

2 answers:

ira [324]3 years ago

8 0

Answer: c. x=2 or x=3

Hope this helped! :)

Roman55 [17]3 years ago

3 0

Answer:

x = 2 or x = 3

Step-by-step explanation:

x = 2 + sqrt(x - 2)

x - 2 = sqrt(x - 2) You could divide both sides by sqrt(x - 2)

sqrt(x - 2) = 1 Square both sides

x - 2 = 1 Add 2 to both sides

x = 3

There is a second way.

x - 2 = sqrt(x - 2) Square

x^2 - 4x + 4 = x - 2 Transfer x - 2 to the left

x^2 - 5x + 6 = 0 Factor

(x - 2)(x-3) = 0 Find the roots.

x - 2 = 0

x = 2

x - 3 = 0

x = 3

We have to check both results.

x = 2 + sqrt(x - 2)

2 = 2 + sqrt(2 -2)

2 = 2 + 0

2 = 2 This seems to work.

x = 2 + sqrt(x - 2)

3 = 2 + sqrt(3 - 2)

3 = 2 + sqrt(1)

3 = 2 + 1

3 = 3 And this works.

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<h3>Further explanation</h3>

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<u>Unknown :</u>

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<h3>Answer details</h3>

Grade: High School

Subject: Physics

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