What two numbers multiplied together equal -1

Question

And the sum could be -17

Answer 1

If the two numbers are x and y, xy=-1 and x+y=-17.

Since y=-1/x, x+y=x-1/x=-17,

x²-1=-17x,

x²+17x-1=0,

x²+17x=1,

x²+17x+(17/2)²=1+(17/2)²=1+289/4=293/4,

(x+(17/2))²=293/4,

x+(17/2)=±√293/2,

x=-(17/2)±√293/2, which produces two possible solutions for x"

x=-8.5±8.5586 (approx), x=0.0586 or x=-17.0586.