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

Given:

Two numbers differ by 4 and their product is 192.

 To do:

We have to find the numbers.

Solution:

Let the two numbers be $x$ and $x+4$.

According to the question,

$x(x+4)=192$

$x^2+4x=192$

$x^2+4x-192=0$

Solving for $x$ by factorization method, we get,

$x^2+16x-12x-192=0$

$x(x+16)-12(x+16)=0$

$(x+16)(x-12)=0$

$x+16=0$ or $x-12=0$

$x=-16$ or $x=12$

If $x=-16$, then $x+4=-16+4=-12$

If $x=12$, then $x+4=12+4=16$

The required numbers are $-16$ and $-12$ or $12$ and $16$. 

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Updated on: 10-Oct-2022

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