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Find Two Numbers Whose Sum is 27 and Product is 182. - Mathematics

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

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Solution

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.

Concept: Solutions of Quadratic Equations by Factorization
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APPEARS IN

NCERT Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.2 | Q 3 | Page 76
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