What two number multiply to 1 and add to 5?

Answer 1

6

Answer 2

Ooh, a puzzle. I like these.

xy=1 AND

x+y=5 ==> y=5-x this step will keep things easier since we will need to substitute

You're going to wind up with a quadratic equation which will give you two numbers.

Substituting, we can have:

y=5-x --> x(5-x)=1 ==> 5x-x2=1 which can be rewritten as

0=x2-5x+1

Boom.

Now to solve this, we go to the quadratic equation. ax2+bx+c

b2-4ac = 25-4(1)(1)=21 I like to solve the inside of the sqrt bracket first

(-b± sqrt (21)) /2a here is the equation with the inside already completed - notice there is a plus/minus sign. there are two equations to be done, one addition, one subtraction.

Since the sqrt(21) is a crazy decimal thing, I won't resolve it into a decimal until the end.

-b+sqrt(21)/2a = 5+sqrt(21)/2

-b-sqrt(21)/2a = 5-sqrt(21)/2

sqrt(21) is approx. 4.583 so we get

5+4.583/2 = 9.583/2 = 4.792 = x

and

5-4.583/2 = .417/2 = .208 = y

Note: the numbers given as x and y are accurate but not 100% because of decimal rounding. This is a good an answer as any and no one should have cause to complain; the answer checks out. :)