The sum of two whole numbers is 18 and their product is 45, the numbers are : 1. 15 and 3 2. -15 and -3 3. -15 and 3 4. 15 and -3

Let numbers be x and y. Given, Sum of whole numbers = 18 ⇒ x + y = 18 ⇒ x = 18 - y ......(1) Product = 45 ⇒ xy = 45 ........(2) Substituting value of x from equation (1) in equation (2), we get : ⇒ (18 - y)y = 45 ⇒ 18y - y 2 = 45 ⇒ y 2 - 18y + 45 = 0 ⇒ y 2 - 15y - 3y + 45 = 0 ⇒ y(y - 15) - 3(y - 15) = 0 ⇒ (y - 3)(y - 15) = 0 ⇒ y - 3 = 0 or y - 15 = 0 ⇒ y = 3 or y = 15. If y = 3, x = 18 - y = 18 - 3 = 15. If y = 15, x = 18 - y = 18 - 15 = 3. Hence, Option 1 is the correct option.

Mathematics

The sum of two whole numbers is 18 and their product is 45, the numbers are :
15 and 3
-15 and -3
-15 and 3
15 and -3

Quadratic Equations

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Answer

Let numbers be x and y.

Given,

Sum of whole numbers = 18

⇒ x + y = 18

⇒ x = 18 - y ……(1)

Product = 45

⇒ xy = 45 ……..(2)

Substituting value of x from equation (1) in equation (2), we get :

⇒ (18 - y)y = 45

⇒ 18y - y² = 45

⇒ y² - 18y + 45 = 0

⇒ y² - 15y - 3y + 45 = 0

⇒ y(y - 15) - 3(y - 15) = 0

⇒ (y - 3)(y - 15) = 0

⇒ y - 3 = 0 or y - 15 = 0

⇒ y = 3 or y = 15.

If y = 3,

x = 18 - y = 18 - 3 = 15.

If y = 15,

x = 18 - y = 18 - 15 = 3.

Hence, Option 1 is the correct option.

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Mathematics

The sum of two whole numbers is 18 and their product is 45, the numbers are :
15 and 3
-15 and -3
-15 and 3
15 and -3

Quadratic Equations

Answer

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