Question

find two numbers sum is 27 and product is 182
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Answer 1

let be,

number one = x

number two = x+1

two number sum of =182

X(27+x) = 182

X2 +27x =182

X2 -27x - 182 =0

X2 - 14x -13x - 182 =0

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

(x-13) (x-14)

x-13=0. x-14=0

x=13. x= 14

number one = x=13

number two = x+1=13+1

= 14

it's your answer

Answer 2

To find: missing numbers

Given : sum of two numbers is $27$ and product is $182$ .

Solution :

• Let , $x$ and $x -27$ be two numbers .
• As per the given data we know that sum of two numbers is $27$ and product is $182$ .  

• Therefore , we know that product is $182$ , represent given conditions as,

        $\begin{array}{l}x(27-x)=182 \\x(27-x)=182 \\27 x-x^{2}=182 \\27 x-x^{2}-182=0 \\x^{2}-27 x+182=0\end{array}$  

      $\begin{array}{l}x^{2}-14 x-13 x+182=0 \\x(x-14)-13(x-14)=0 \\(x-13)(x-14)=0 \\x-13=0 \text { and } x-14=0 \\x=13 \text { and } x=14\end{array}$

Hence , required missing numbers are , $13$ and $14$ .