Two number differ by 4 and their product is 192. Find the numbers… - Vidyadip

Question

Two number differ by $4$ and their product is $192$. Find the numbers.

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Answer

Let first number $= x$
Then second number $= x - 4$
According to the condition,
$\Rightarrow x(x - 4) = 192$
$\Rightarrow x^2 - 4x - 192 = 0$
$\Rightarrow x^2 - 16x + 12x - 192 = 0$
$\Rightarrow x(x - 16) + 12(x - 16) = 0$
$\Rightarrow (x - 16)(x + 12) = 0$
Either $x - 16 = 0$, then $x = 16$
Or $x + 12 = 0$, then $x = -12$

If $x = 16$, then

First number $= 16$ and second number $= 16 - 4 = 12$

If $x = -12$, then

First number $= -12$ and second number $= -12 - 4 = -16$

Hence numbers are $16, 12$ or $-12, -16$

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