Question

find two number whose sum is 27and product is 182​

Answer 1

Step-by-step explanation:

Let the first number be x then the second number will be 27 – x.

$x(27-x) =182$$

→ 27x - x² = 182

→ x - 27x + 182 = 0

→ x - 13x - 14x + 182 = 0

→ x(x – 13) – 14(x - 13) = 0

→ (x- 14)(x - 13) = 0

→ x= 14, 13

If the first number is 14, then the second number is 13 and if the first number is 13. then the second number is 14.

Answer 2

Given -

• Sum of two numbers is 27.
• Product of two numbers is 182.

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To find -

• Required two numbers.

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Solution -

• Let the required numbers be x and y.

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★ According to the question

→ x + y = 27⠀⠀... [1]

and,

→ xy = 182

→ x = 182/y

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★ Putting the value of x in eq[1]

→ 182/y + y = 27

→ 182 + y² = 27y

→ y² - 27y + 182 = 0

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By middle term spiliting

→ y² - 13y - 14y + 182 = 0

→ y(y - 13) - 14(y - 13) = 0

→ (y - 13) (y - 14) = 0

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★ We get

• y = 13
• y = 14

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★ Putting the values of y in eq[1]

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When y = 13

• x = 14

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When y = 14

• x = 13

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Hence,

• Required numbers 13 and 14.

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