Question

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

Answer 1

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

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

$x=\frac{-2(+/-)\sqrt{8}} {-2}$

$x1=\frac{2-\sqrt{8}} {2}=1-\sqrt{2}$

$x2=\frac{2+\sqrt{8}} {2}=1+\sqrt{2}$

therefore

the answer is

the positive solution is $1+\sqrt{2}$

Answer 2

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)