Question

If the sum of two numbers is 13 and their product is 42,determine the numbers.

Answer 1

Answer:

See the attachment below for answer:-

Answer 2

The two numbers are - 6 and 7.

Let the two numbers be represented as X and Y.

Given in question is sum of two numbers is 13, hence it will be represented as -

X + Y = 13

Given in question say, product of two numbers is 42, thus equation will be represented as -

X*Y = 42

Y = 42/X

X + 42/X = 13

X² + 42 = 13X

X² - 13X + 42 = 0

X² - 6X - 7X + 42 = 0

X(X - 6) - 7(X - 6) = 0

(X- 6) (X - 7) = 0

X = 6 and 7.

Now, to calculate Y, keeping the values in original equation -

X + Y = 13

Y = 13 - X

Y = 13 - 6

Y = 7

X + Y = 13

Y = 13 - X

Y = 13 - 7

Y = 6

Hence, Y = 6 and 7

Now, X can be 7 then value of Y will be 6 and X can be 6 then value of Y will be 7.