Question

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

Answer 1

Let the first number be x and the second number is 27 - x.

Therefore, their product = x (27 - x)

It is given that the product of these numbers is 182.

Therefore,

x(27 - x) = 182

⇒ x2 – 27x + 182 = 0

⇒ x2 – 13x - 14x + 182 = 0

⇒ x(x - 13) -14(x - 13) = 0

⇒ (x - 13)(x -14) = 0

Either

x = -13 = 0 or x - 14 = 0

⇒ x = 13 or x = 14

If first number = 13,

then

Other number = 27 - 13 = 14

If first number = 14,

then

Other number = 27 - 14 = 13

Therefore, the numbers are 13 and 14.

Answer 2

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Here you Go.

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• Let the first no. be "a"

• Then the second no. = (27 - a)

Product = 182

• a(27 - a) = 182

• 27a - a² = 182

• a² - 27a + 182 = 0

• a² - 14a - 13a + 182 = 0

• a(a - 14) - 13(a - 14) = 0

• (a - 14)(a - 13) = 0

When (a - 14) = 0

----> a = 14

----> 27 - a = 13

When (a - 13) = 0

----> a = 13

----> 27 - a = 14

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Conclusion

.

The required numbers are :-

${\boxed{\huge{\bold{14\:and\:13}}}}$

.

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I Hope This Will Help You.