Question

What is the positive solution to the equation 0 = –x2 + 2x + 1?

Answer 1

The equation
`0=-x^2+2x+1` is equivalent to the equation
`x^2-2x-1=0.`

Solve this equation:

1.
`D=b^2-4ac=(-2)^2-4\cdot 1\cdot (-1)=4+4=8.`

2.
`√(D)=√(8)=2√(2).`

3.

`x_1=(-b+√(D))/(2a)=(2+2√(2))/(2)=1+√(2)`

and

`x_2=(-b-√(D))/(2a)=(2-2√(2))/(2)=1-√(2).`

4. Since
`√(2)>1,` you have that
`1-√(2)<0.`

Answer: the positive solution is
`x=1+√(2).`