Question 927004
Write a quadratic equation with leading coefficient of 1 having as its two roots, the numbers obtained by increasing each root of x^2-2x-5 = 0 by the reciprocal of the other.
Find roots of  x^2 - 2x - 5 = 0 using the "completing the square" method
x^2 - 2x + ___  = 5
Find half of the value of 2 and square it, add to both sides
x^2 - 2x + 1 = 5 + 1
(x-1)^2 = 6
x - 1 = +/- {{{sqrt(6)}}}
two solutions
x = 1 + {{{sqrt(6)}}}
x = 1 - {{{sqrt(6)}}}
"Find two roots, obtained by increasing each root of by the reciprocal of the other."
Using a calc
{{{1 + sqrt(6)}}} + {{{1/(1-sqrt(6))}}} = 2.75959
{{{1 - sqrt(6)}}} + {{{1/(1+sqrt(6))}}} = -1.15959
FOIL
(x-2.75959)(x+1.15959) = x^2 + 1.15959x - 2.75959x - 3.20000
y = x^2 - 1.6x - 3.2, is the equation