Question

Two numbers differ by 3 and a product is 54. Find the number?

Answer 1

the no.s are 9 and 6.

Answer 2

Given:

two numbers difference are 3and product is 54

To find:

Both the numbers

Solution:

Let x and y be the two numbers

by the given condition, x-y=3

and xy=54

Rewrite xy=54 by x=$\frac{54}{y}$

put the value of x in x-y=3

$\frac{54}{y}$-y=3

take L.C.M

$\frac{54-y^{2} }{y}$=3

cross multiply

54-y²=3y

y²+3y-54=0

split the middle term

y²+(9-6)y-54=0

y²+9y-6y-54=0

take common outside

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

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

y-6=0,y+9=0

y=6,y=-9

⇒number can't be negative

∴y=6

by x-y=3

x-6=3

x=3+6

x=9

Hence, numbers are 6,9