Question

What two numbers satisfy the conditions of adding up to 3 and multiplying to 1?

a) 2 and 1
b) 3 and 0
c) 4 and -1
d) -1 and -2

Answer 1

To find two numbers that satisfy the conditions, we can set up a system of equations and solve for the variables. The equations are x + y = 3 and xy = 1. By substituting and solving, we find that the two numbers are (3 + √5)/2 and (3 - √5)/2.

Step-by-step explanation:

To find two numbers that satisfy the conditions of adding up to 3 and multiplying to 1, we can set up a system of equations. Let's call the numbers x and y:

x + y = 3 xy = 1

From the first equation, we can solve for one variable in terms of the other. Let's solve for x: x = 3 - y

Now substitute this expression for x in the second equation (3 - y)y = 1

Expanding and rearranging, we get: y^2 - 3y + 1 = 0

Using the quadratic formula, we can solve for y: y = (3 ± √5)/2

These two values of y correspond to the two possible values of x. Therefore, the two numbers that satisfy the conditions are (3 + √5)/2 and (3 - √5)/2.