Product of two numbers is 10 and the sum of the two numbers is 7. Then the larger of the two numbers is:

Question: Product of two numbers is 10 and the sum of the two numbers is 7. Then the larger of the two numbers is:

Solution:
Let the two numbers be x and y.
According to the question,
x + y = 7 ........(i)
xy = 10 .........(ii)

We know,
(x - y)² = (x + y)² - 4xy
⇒ (x - y)² = (7)² - 4(10)
⇒ (x - y)² = 49 - 40
⇒ (x - y)² = 9
⇒ x - y = √9
⇒ x - y = 3 ........(iii)

Now, adding equations (i) and (iii):
(x + y) + (x - y) = 7 + 3
⇒ 2x = 10
⇒ x = 5

Putting the value of x in equation (i):
5 + y = 7
⇒ y = 7 - 5
⇒ y = 2

Comparing the two numbers 5 and 2, the larger number is 5.

∴ The larger of the two numbers is 5