What is the answer to sqrt(x-1)+(x-1)^2=0 ?

The answer to sqrt(x-1)+(x-1)^2=0 is x=1

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sqrt(x-1)+(x-1)^2=0

x - 1 + (x - 1)^{2} = 0

x = 1

Solution steps

x - 1 + (x - 1)^{2} = 0

Expand

x - 1 + (x - 1)^{2} : x - 1 + x^{2} - 2 x + 1

x - 1 + x^{2} - 2 x + 1 = 0

Remove square roots

x - 1 = x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

Solve

x - 1 = x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1 : x = 1, x = 2

x = 1, x = 2

Verify Solutions:

x = 1

True

, x = 2

False

The solution is

x = 1

8 - x = 2 + 2 x + 3

x^{2} - x = 6

2 x + 2 = 3 + 2 x - 1

10 = 5 - x^{2} + 10

What is the answer to sqrt(x-1)+(x-1)^2=0 ?
The answer to sqrt(x-1)+(x-1)^2=0 is x=1
Solve for x: sqrt(x-1)+(x-1)^2=0
The solution is x=1