Question

ven in Example 1. 2. Find two numbers whose sum is 27 and product is 182. Find​

Answer 1

Answer:

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Step-by-step explanation:

Let us consider one of the numbers to be x. Then the other number will be 27 - x.

The product of the two numbers is given as 182

This can be written in the form of the following quadratic equation:

x(27 - x) = 182

x(27 - x) = 182

27x - x2 = 182

27x - x2 - 182 = 0

x2 - 27 x + 182 = 0 [Rearranging the terms and multiplying both sides by negative sign]

x2 - 14x - 13x + 182 = 0

x (x - 14) - 13 (x - 14) = 0

(x -13) (x - 14) = 0

x - 13 = 0 and x - 14 = 0

x = 13 and x = 14

Therefore, the required numbers are 13, 14.

Answer 2

The numbers are 13 and 14

Given :

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

To find :

The two numbers

Solution :

Step 1 of 2 :

Form the equation to find the numbers

Here it is given that the two numbers whose sum is 27

Let the numbers are x and 27 - x

Now their product is 182

By the given condition

$\displaystyle \sf{ x(27 - x) = 182}$

Step 2 of 2 :

Find the numbers

$\displaystyle \sf{ x(27 - x) = 182}$

$\displaystyle \sf{ \implies 27x - {x}^{2} = 182 }$

$\displaystyle \sf{ \implies {x}^{2} - 27x + 182 = 0}$

$\displaystyle \sf{ \implies {x}^{2} - (13 + 14)x + 182 = 0}$

$\displaystyle \sf{ \implies {x}^{2} - 13x - 14x + 182 = 0}$

$\displaystyle \sf{ \implies x(x - 13) - 14(x - 13) = 0}$

$\displaystyle \sf{ \implies (x - 13) (x - 14) = 0}$

When x - 13 = 0 we have x = 13

First number = 13

Second number = 27 - 13 = 14

When x - 14 = 0 we have x = 14

First number = 14

Second number = 27 - 14 = 13

Hence two numbers are 13 and 14

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