Question

Use a quadratic equation to find two real numbers with a sum of 31 and a product of 210

Answer 1

Answer:

If the sum of two numbers is 31 and their product is 210, then find the absolute difference between the numbers

Answer 2

The two numbers are 21 and 10

Given:

Sum of two numbers = 31

Product of two numbers = 210

To Find:

We need to find the values of the two numbers

Solution:

Let the two numbers be x and y

according to the question-

x + y = 31

⇒ x = 31 - y

and xy = 210

⇒ (31 - y)y = 210

31y - y² = 210

y² - 31y + 210 = 0

y² - 21y - 10y + 210 = 0

y(y - 21) - 10(y - 21) = 0

(y - 10)(y - 21) = 0

⇒ y = 10 or 21

Thus, x = (31 - 10) or (31 - 21)

x = 21 or 10

Hence, we get that the two numbers are 21 and 10

#SPJ3