Question

find two consecutive positive even integer whose products is288

Answer 1

Let the two consecutive positive integer be x and x+2
According to the given condition,
X(x+2)=288
X^2+2x-288=0
x^2+18x-16x-288=0
x(x+18)-16(x+18)=0
(x+18)(x-16)=0
x+18=0 or x-16=0
x=-18 or x=16
Since the integers are positive
We wil take x=16
Therefore another positive integer will be 16+2=18
Hence the positive integers are 16 and 18

Answer 2

Answer:

Let,

the two consecutive positive integer be x and

x+2.

A.T.Q,

x . ( x+2) = 288.

or, x^2 +2x - 288 =0

or, x^2 + 18x - 16x - 288 =0

or, x( x +18) - 16( x+18) =0

or, (x-16) ( x +18)=0

Now,

x-16 =0

or, x=16

And,

x+18=0

or, x = - 18 .

Here, integers are positive

so,

x=16

and,

x+2= 16+2 =18.

Hence, the required solution is 16 and 18