If the sum of two natural numbers is 8 and the product is 15, then fin

1.	If the sum of two natural numbers is 8 and the product is 15, then find numbers.
Answer» Let the first natural number be x. Sum of two natural numbers is 8 then other natural numbers will be 8 – x. According to question. Product of both natural numbers = 15 ⇒ x (8 – x) = 15 ⇒ 8x – x² = 15 ⇒ x² – 8x + 15 = 0 ⇒ x² – (5 + 3)x + 15 = 0 ⇒ x² – 5x – 3x + 15 = 0 ⇒ (x² – 5x) – (3x – 15) = 0 ⇒ x (x – 5) – 3 (x – 5) = 0 ⇒ (x – 5) (x – 3) = 0 ⇒ x – 5 = 0 or x – 3 = 0 ⇒ x = 5 or x = 3 Thus, if First natural no. = 5 then Second natural no. = 8 if First natural no. = 3 or Second natural no. = 8

If the sum of two natural numbers is 8 and the product is 15, then find numbers.

Answer»

Let the first natural number be x.

Sum of two natural numbers is 8 then other natural numbers will be 8 – x.

According to question.

Product of both natural numbers = 15

⇒ x (8 – x) = 15

⇒ 8x – x² = 15

⇒ x² – 8x + 15 = 0

⇒ x² – (5 + 3)x + 15 = 0

⇒ x² – 5x – 3x + 15 = 0

⇒ (x² – 5x) – (3x – 15) = 0

⇒ x (x – 5) – 3 (x – 5) = 0

⇒ (x – 5) (x – 3) = 0

⇒ x – 5 = 0 or x – 3 = 0

⇒ x = 5 or x = 3

Thus, if First natural no. = 5

then Second natural no. = 8

if First natural no. = 3

or Second natural no. = 8