# Ex.4.2 Q3 Quadratic Equations Solutions - NCERT Maths Class 10

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## Question

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

Video Solution
Ex 4.2 | Question 3

## Text Solution

What is known?

(i) Sum of two numbers is $$27.$$

(ii) Product of two numbers is $$182.$$

What is Unknown?

Two numbers.

Reasoning:

Let one of the numbers be $$x$$. Then the other number will be

$$x +$$ other number $$= 27$$

Other number $$= 27 – x$$

Product of the two numbers $$= 182$$

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

$x\left( {27 - x} \right) = 182$

Steps:

\begin{align}x\left( {27 - x} \right) &= 182\\27x - x &= 182\\27x - x - 182 &= 0\\x - 27x + 182 &= 0\\x - 14x-13x + 182 &= 0\\x\left( {x - 14} \right)-13\left( {x - 14} \right) &= 0\\\left( {x - 13} \right)\left( {x - 14} \right) &= 0\\x-13 = 0 & \qquad x-14 = 0\\x = 13 & \qquad x = 14\end{align}

The numbers are $$13,\, 14.$$

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