9. The sum of two numbers is 25 and whose product is 156. find the two numbers.
2 answers:
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,
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.
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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