Question
Find two numbers whose sum is 27 and product is 182.
✓
Answer
Let the two numbers be x, 27 - x.According to the question
$x(27-x)=182 $
$\Longrightarrow 27 x-x^2-182=0 $
$\Longrightarrow x^2-27 x+182=0 $
$\Longrightarrow x^2-13 x-14 x+182=0 $
$\Longrightarrow x(x-13)-14(x-13)=0 $
$\Longrightarrow(x-13)(x-14)=0 $
$\text { Either } x-13=0 \text { or } x-14=0 $
$\Longrightarrow x=13,14$
Hence, the required numbers are 13,14
$x(27-x)=182 $
$\Longrightarrow 27 x-x^2-182=0 $
$\Longrightarrow x^2-27 x+182=0 $
$\Longrightarrow x^2-13 x-14 x+182=0 $
$\Longrightarrow x(x-13)-14(x-13)=0 $
$\Longrightarrow(x-13)(x-14)=0 $
$\text { Either } x-13=0 \text { or } x-14=0 $
$\Longrightarrow x=13,14$
Hence, the required numbers are 13,14
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