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

The answer to sqrt(2-x)=2-x^2 is x=1,x=(1-sqrt(5))/2

Solve for x: sqrt(2-x)=2-x^2

The solution is x=1,x=(1-sqrt(5))/2

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2 - x = 2 - x^{2}

x = 1, x = \frac{1 - 5}{2}

Decimal Notation

x = 1, x = - 0.61803 \dots

Solution steps

2 - x = 2 - x^{2}

Square both sides:

2 - x = 4 - 4 x^{2} + x^{4}

2 - x = 4 - 4 x^{2} + x^{4}

Solve

2 - x = 4 - 4 x^{2} + x^{4} : x = 1, x = - 2, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

x = 1, x = - 2, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Verify Solutions:

x = 1

True

, x = - 2

False

, x = \frac{1 + 5}{2}

False

, x = \frac{1 - 5}{2}

True

The solutions are

x = 1, x = \frac{1 - 5}{2}

\frac{x}{x + 1 + 1} = x + 1 - 1

3 - 8 x^{2} = 2 x

2 x - 2 x + 3 = 6

x - 10 = x - 1

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