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Yuki888 [10]
2 years ago
6

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

Mathematics
2 answers:
lord [1]2 years ago
4 0

Answer:

x = 12

y = 13

Step-by-step 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.

natka813 [3]2 years ago
4 0

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 :>

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