What is the answer to sqrt(1-|x-2|)=x-2 ?

The answer to sqrt(1-|x-2|)=x-2 is x=(3+sqrt(5))/2

Solve for x: sqrt(1-|x-2|)=x-2

The solution is x=(3+sqrt(5))/2

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1 - ∣ x - 2 ∣ = x - 2

x = \frac{3 + 5}{2}

Decimal Notation

x = 2.61803 \dots

Solution steps

1 - ∣ x - 2 ∣ = x - 2

Square both sides:

1 - ∣ x - 2 ∣ = x^{2} - 4 x + 4

1 - ∣ x - 2 ∣ = x^{2} - 4 x + 4

Solve

1 - ∣ x - 2 ∣ = x^{2} - 4 x + 4 : x = \frac{5 - 5}{2} or x = \frac{3 + 5}{2}

x = \frac{5 - 5}{2}, x = \frac{3 + 5}{2}

Verify Solutions:

x = \frac{5 - 5}{2}

False

, x = \frac{3 + 5}{2}

True

The solution is

x = \frac{3 + 5}{2}

(x - 3)^{\frac{2}{3}} = 16

x = - x + 20

t^{- \frac{1}{3}} = \frac{1}{2}

6 x - 5 = 7

x + x - 12 = 0

What is the answer to sqrt(1-|x-2|)=x-2 ?
The answer to sqrt(1-|x-2|)=x-2 is x=(3+sqrt(5))/2
Solve for x: sqrt(1-|x-2|)=x-2
The solution is x=(3+sqrt(5))/2