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

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

Solve for x: x^2-2x-2sqrt(x^2-2x+2)=1

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

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x^{2} - 2 x - 2 x^{2} - 2 x + 2 = 1

x = 1 + 22, x = 1 - 22

Decimal Notation

x = 3.82842 \dots, x = - 1.82842 \dots

Solution steps

x^{2} - 2 x - 2 x^{2} - 2 x + 2 = 1

Remove square roots

4 x^{2} - 8 x + 8 = x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1

Solve

4 x^{2} - 8 x + 8 = x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1 : x = 1, x = 1 + 22, x = 1 - 22

x = 1, x = 1 + 22, x = 1 - 22

Verify Solutions:

x = 1

False

, x = 1 + 22

True

, x = 1 - 22

True

The solutions are

x = 1 + 22, x = 1 - 22

7 - v = v - 35

x - 3 = x - 3

23 x + 105 = x + 9

6 x - 8 = 4

10 u - 16 = u

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