Find two numbers such that their sum and their product is -1

Question

Please, hurry up. I need it now??

Answer 1

Hi Kenneth:

If you need two numbers, x and y, with a sum AND product of -1, try setting equations that describe both conditions:

x+y=-1
xy=-1

This is two equations with two unknowns, a system we can solve. If, for example, you solve one equation for x in terms of y, then substitute that expression into the other equation -- to make that second equation only in terms of y -- you can then solve for y.

It turns out to be a quadratic equation in y, which you can use the quadratic formula to solve.  I hope this puts you on the right path, but if you have more questions, just let me know.

Answer 2

Let your numbers be x and y

 

x + y = -1    their sum is -1

xy = -1        their product is -1

 

From equation 2 we can get y = -1/x

Substitute that into equation 1

 

x -1/x = -1   multiply all by x

x² -1 = -x     add x to both sides

x² + x - 1 = 0

 

Using the quadratic equation

x = [-b±√(b²-4ac)]/2a    a=1, b=1, c= -1

 

x = [-1 ±√(1²-4(1)(-1))]/2(1)

x = [-1 ±√(1+4)]/2

x = (-1 ±√5)/2

 

Answer 1:

x = (-1+√5)/2

y = -1/x = -2/(-1+√5)

 

Answer 2:

x = (-1-√5)/2

y = -1/x = -2/(-1-√5) = 2/(1+√5)