Question

3. Find two numbers whose sum is 27 and product is 182​

Answer 1

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Let the two numbers be x and y

■ According to statement

Sum of two numbers is 27

⟹ x + y = 27

⟹ y = 27 - x .........(1)

■ According to statement again,

Product of two numbers is 182.

⟹ xy = 182

On using (1) we get,

x(27 - x) = 182

⟹ 27x - x² = 182

⟹ x² - 27x + 182 = 0

⟹ x² - 14x - 13x + 182 = 0

⟹ x(x - 14) - 13(x - 14) = 0

⟹ (x - 14)(x - 13) = 0

⟹ x - 14 = 0 or x - 13 = 0

⟹ x = 14 or x = 13

⟹ y = 13 or y = 14

So two numbers are 13 and 14.

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Answer 2

A n s w e r

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G i v e n

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• Sum of two numbers is 27

• Product of the same two numbers is 182

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F i n d

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• The two numbers

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S o l u t i o n

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• Let the first number be "a"

• Let the second number be "b"

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$\underline{\bold{\texttt{Sum of the two numbers :}}}$

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Given that sum of two numbers is 27

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➠ a + b = 27 ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Product of the two numbers :}}}$

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Given that the product of the same two numbers is 182

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➠ a × b = 182

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➜ $\sf a = \dfrac { 182 } { b }$ ⚊⚊⚊⚊ ⓶

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⟮ Putting the values of a from ⓶ to ⓵ ⟯

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➜ a + b = 27

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➜ $\sf \dfrac { 182 } { b } + b = 27$

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➜ $\sf \dfrac { 182 + b ^2 } { b } = 27$

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➜ 182 + b² = 27b

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➜ b² - 27b + 182 = 0

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➜ b² - 13b - 14b + 182 = 0

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➜ b(b - 13) -14(b - 13) = 0

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➜ (b - 13)(b - 14) = 0

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• b = 13
• b = 14

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When b = 13

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⟮ Putting b = 13 in ⓵ ⟯

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➜ a + b = 27

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➜ a + 13 = 27

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➜ a = 27 - 13

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➨ a = 14

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• Hence b = 13 and a = 14

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When b = 14

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⟮ Putting b = 14 in ⓵ ⟯

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➜ a + b = 27

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➜ a + 14 = 27

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➜ a = 27 - 14

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➨ a = 13

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• Hence b = 14 and a = 13

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∴ The two numbers are 13 , 14 Or 14 , 13