Answer:
Explanation:
To find two numbers that satisfy both conditions - their sum is 10 and their product is 22 - you can set up a system of equations and solve for the numbers. Let's call the two numbers x and y.
1. The first condition: Their sum is 10.
x + y = 10
2. The second condition: Their product is 22.
xy = 22
Now, you can solve this system of equations. One way to do it is by solving the first equation for one of the variables and substituting it into the second equation:
From the first equation, you can express x as x = 10 - y.
Now, substitute this into the second equation:
(10 - y)y = 22
Expand and simplify:
10y - y^2 = 22
To solve for y, move everything to one side of the equation:
y^2 - 10y + 22 = 0
Now, you can solve this quadratic equation for y. You can use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -10, and c = 22.
y = (-(-10) ± √((-10)^2 - 4(1)(22))) / (2(1))
y = (10 ± √(100 - 88)) / 2
y = (10 ± √12) / 2
Now, calculate the two possible values for y:
1. y = (10 + √12) / 2
2. y = (10 - √12) / 2
Solving for y:
1. y ≈ 7.82 (rounded to two decimal places)
2. y ≈ 2.18 (rounded to two decimal places)
Now that you have the two possible values of y, you can find the corresponding values of x using the first equation:
1. If y ≈ 7.82, then x ≈ 10 - 7.82 ≈ 2.18
2. If y ≈ 2.18, then x ≈ 10 - 2.18 ≈ 7.82
So, the two pairs of numbers that satisfy the conditions are approximately (7.82, 2.18) and (2.18, 7.82).