Question

Two positive no.differ by 3 and their product is 54 find the no.

Answer 1

Hi ,

Let x and ( x - 3 ) are two positive numbers.

according to the problem given ,

product of two numbers = 54

x( x - 3 ) = 54

x² - 3x - 54 = 0

x² - 9x + 6x - 54 = 0

x( x - 9 ) + 6 ( x - 9 ) = 0

( x - 9 )( x + 6 ) = 0

Therefore ,

x - 9 = 0 or x + 6 = 0

x = 9 or x = -6

But x is a positive integer .

We take x = 9.

Required two numbers are

x = 9 ,

x - 3 = 9 - 3 = 6

( 9 , 6 )

I hope this helps you.

: )

Answer 2

Let,
Two positive numbers are :-

• x
• x - 3

============

Their product = 54

x × (x - 3) = 54

x² - 3x - 54 = 0

x² - (9-6)x - 54 = 0

x² - 9x+ 6x - 54 = 0

x (x - 9) + 6(x - 9) = 0

(x - 9)(x + 6) = 0

By zero product rule,

x = 9 OR x = -6


Taking positive value of x [given in question]

x = 9

Now,

Two positive number

x=9
x - 3 = 9-3 = 6