Question

2 numbers differer by 3 then product is 54 find the number

Answer 1

One number be x
Therefore other number will be 3 + x
Product is 54 so......
x(3 + x) = 54
3x + x^2 = 54
x^2 + 3x - 54 = 0
x^2 + 9x - 6x - 54 = 0
x(x + 9) - 6(x + 9) = 0
x-6 = 0 or x + 9 = 0
x = 6 or x = -9
Therefore one number is 6 or -9.
Other number is x+3 which is.....
6 +3 = 9 or -9+3 = -6.
Thanks.

Answer 2

let the two no. be x and y in which x one is greater than y. then ,
x-y=3
xy=54
we know that
$(x - y)^{2} = {x }^{2} + {y}^{2} - 2xy$
. .......1
now
$(x + y) {}^{2} = {x}^{2} + y { }^{2} + 2xy \\ x {}^{2} + y {}^{2} = (x + y) {}^{2} - 2xy$
. ........2
now putting equation 2 in 1 we get
$(x - y) {}^{2} = (x + y)^{2} - 4xy$
putting the value of x-y and xy in above equation we get...
$3 {}^{2} = (x + y) {}^{2} - 4 \times 54$
or

$(x + y) {}^{2} = 225$
or
$x + y = \sqrt{225}$
or
$x + y = 15$
further
$x - y = 3$
...ATQ

solving just above two reaction we get
$2x = 18$
or
$x = 9$
now since x-y=3
putting the value of x above we will get y =6
hence
$x = 9 \\ and \\ y = 6$