The positive solution to the equation [tex]-x^{2} +2x+1=0[/tex] is [tex]x=1+\sqrt{2}[/tex].
Given quadratic equation is:
[tex]-x^{2} +2x+1=0[/tex]
The general form of a quadratic equation is [tex]ax^{2} +bx+c=0[/tex] and [tex]a\neq 0[/tex].
On comparing with general form of quadratic equation
a = -1
b = 2
c = 1
So, from the Shreedharacharya formula,
[tex]x = \frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
[tex]x = \frac{-2+-\sqrt{2^{2} -4(-1)(1)} }{2*(-1)}[/tex]
[tex]x = 1-\sqrt{2} \\x=1+\sqrt{2}[/tex]
as [tex]x = 1-\sqrt{2}[/tex] is negative
So, the positive solution is [tex]x=1+\sqrt{2}[/tex]
Therefore, the positive solution to the equation [tex]-x^{2} +2x+1=0[/tex] is [tex]x=1+\sqrt{2}[/tex].
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