Question

9. The sum of two numbers is 25 and whose product is 156. find the two numbers.​

Answer 1

x = 12

y = 13

Explanation:

Let's assume the two numbers as x and y.

The sum of the two numbers is 25

So,

• x+y = 25
• y = 25 - x

The product of the two numbers is 156

• xy = 156
• x(25 - x) = 156
• 25x - x² = 156
• x² - 25x + 156 = 0
• x² - 13x - 12x - 156 = 0
• (x - 12) • (x - 13) = 0
• x - 13 = 0
• x = 13
• x - 12 = 0
• x = 12

Hence, the two numbers are 13 and 12.

Answer 2

Example: we have to find 2 number : a and b

• a + b = 25 ⇒ a = 25 - b (1)
• a × b = 156 ⇒ a = 156/b (2)

(1)(2) ⇒ 156/b = 25 - b

⇒ 156/b - 25 + b = 25 - b - 25 + b

⇒ b - 25 + 156/b = 0

⇒ (b - 25 + 156/b) × b = 0 × b = 0

⇒ b² - 25b + 156 = 0

⇒ b² - (13b + 12b) + 156 = 0

⇒ b² - 13b - 12b + 156 = 0

⇒ (b² - 13b) + (- 12b + 156) = 0

⇒ b(b - 13) - 12(b - 13) = 0

⇒ (b - 13)(b - 12) = 0

⇒ b = 13 or b = 12

• if b = 12 => a = 25 - 12 = 13

• if b = 13 => a = 25 - 13 = 12

Answer: 12 and 13

OK done. Thank to me :>