Write two numbers which differ by 3 and whose product is 54.

Given :

Difference between two numbers $= 3$.

Product of those numbers $= 54$.

To do :

We have to find the numbers.

Solution :

Let the one number be $= a$

So, second number $= a - 3$

Now,

$a \times (a - 3) = 54$

$a^2 - 3a = 54$

$a^2 - 3a - 54 = 0$

$a^2 - 9a + 6a - 54 = 0$

$a(a-9) + 6(a - 9) = 0$

$(a+6)(a-9) = 0$

So,

$a = 9$ or $-6$

But a could not be negative so $a =9$.

1st number $= a = 9$

2nd number $= a - 3 = 9 - 3 = 6$

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Updated on: 10-Oct-2022

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