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Answer 1

QUESTION:

Find the two numbers whose sum is 27 and product is 182.

ANSWER:

The two numbers are 13 and 14

GIVEN:

Sum = 27

Product = 182

TO FIND:

The two numbers

EXPLANATION:

Let the numbers be x and y

x + y = 27

x = 27 - y

xy = 182

Substitute x = 27 - y in xy = 182

(27 - y)y = 182

27y - y² = 182

y² - 27 + 182 = 0

By splitting the middle term

y² - 14y - 13y + 182 = 0

y(y - 14) - 13(y - 14)

(y - 14)(y - 13)

y = 14 (or) 13

When y = 13 , x = 14

When y = 14 , x = 13

Hence the two numbers are 13 and 14.

VERIFICATION:

x + y = 13 + 14 = 27

xy = 13 × 14 = 182

Hence our verified answer.