Question

Two numbers differed by 3 and their product is 54. find the numbers.

Answer 1

Let the two numbers be x and y with x >y

$x - y = 3 \: \: \: \: \: \: xy = 54$
$y = \frac{54}{x}$
$\frac{ {x}^{2} - 54 }{x} = 3$
${x }^{2} - 3x - 54 = 0$
$(x - 9)(x + 6) = 0$
$x = 9$
$y = 6$

Answer 2

Given:

Two numbers differed by 3 and their product is 54.

To find out:

Find the numbers?

Solution:

Let the two numbers be x and y .

★According to the first condition,

Difference if the two number = 3

➠ x - y = 3

➠ y = x - 3 ...............( i )

★ According to the second condition,

➠ xy = 54 ................( ii )

Substituting y = x - 3 from ( i ) and ( ii ), we get

x (x-3) = 54

➠ x² - 3x = 54

➠ x² - 3x - 54 = 0

➠ x² - 9x + 6x - 54 = 0

➠ x ( x - 9 ) + 6 ( x - 9 ) = 0

➠ ( x - 9 ) ( x + 6 ) = 0

➠ x = 9 and x = -6

On putting x = 9 in equation ( i ) , we have

y = 9 - 3 = 6

On putting x = -6 in equation ( i ) , we get

y = -6 - 3 = -9

Hence, the numbers are 9 and 6 or -9 and-6 .