The product of two positive numbers is 35 and their difference is 2. What is the sum of the two numbers?
what the answer?
whats the answer
To find the sum of the two numbers, we first need to determine what those two numbers are. Let's call them x and y.
Given that the product of the two numbers is 35, we have the equation: x * y = 35.
We are also given that the difference between the two numbers is 2. This gives us another equation: x - y = 2.
To find the values of x and y, we can use substitution or elimination method.
Let's solve the second equation for x: x = y + 2.
Substituting this value of x into the first equation, we get: (y + 2) * y = 35.
Expanding the equation, we have: y^2 + 2y = 35.
Rearranging the equation to form a quadratic equation: y^2 + 2y - 35 = 0.
We can solve this quadratic equation using factoring, completing the square, or using the quadratic formula.
Factoring this quadratic equation, we have: (y + 7) * (y - 5) = 0.
Setting each factor to zero, we get two possible values for y: y + 7 = 0 (y = -7) or y - 5 = 0 (y = 5).
Since we are looking for positive values for x and y, we discard the negative value, y = -7.
Therefore, y = 5.
Substituting this value back into x = y + 2, we find x = 7.
So we have x = 7 and y = 5.
To find the sum of the two numbers, x + y, we simply add these values together: 7 + 5 = 12.
Therefore, the sum of the two numbers is 12.
In summary:
- We solved the equations x * y = 35 and x - y = 2 simultaneously to find the values of x and y.
- By substituting the value of x into the first equation, we obtained a quadratic equation.
- We solved the quadratic equation and found the values of y.
- Substituting the value of y back into x = y + 2, we obtained the value of x.
- Finally, we found the sum of the two numbers by adding x and y together, which gave us 12.