Question

The solutions of `y^2+by+c=0` are the reciprocals of the solutions of `x^2-7x+12=0`. Find the value of b+c?

Answer 1

`b+c=-1/2`

Explanation:

`(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1x_2`
`(y-1/x_1)(y-1/x_2) = y^2-(x_1+x_2)/(x_1x_2)y+1/(x_1x_2)`

so we have

`12c=(x_1x_2)/(x_1x_2)=1->c=1/12`

and `x_(1,2) = (7pm sqrt(49-48))/2={3,4}` so

`b=-(3+4)/12=-7/12` and finally

`b+c=-1/2`