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

Advertisement Remove all ads

#### 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

⇒ *x*^{2} – 27*x* - 182 = 0

⇒ *x*^{2} – 13*x* - 14*x* + 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

Is there an error in this question or solution?

#### APPEARS IN

Advertisement Remove all ads