Question

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

Answer 1

x = [ -2 (+ or -) sqrt ( 4 - 4 * -1 * 1) ] / -2 = -2 + sqrt(8)/-2 = 1 + or - sqrt(2)

so the postive root is

1+ sqrt(2)

Answer 2

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

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

so

`a=-1\\b=2\\c=1`

substitute in the formula

`x=\frac{-2(+/-)\sqrt{2^(2)-4(-1)(1)}} {2(-1)}`

`x=\frac{-2(+/-)√(8)} {-2}`

`x1=\frac{2-√(8)} {2}=1-√(2)`

`x2=\frac{2+√(8)} {2}=1+√(2)`

therefore

the answer is

the positive solution is
`1+√(2)`