Question

twenty times a positive integer is less then its square by 96 what is the intiger

Answer 1

let the positive integer be x
According to the question,

x²-20x=96
x²-20x-96=0
x²-24x+4x-96=0
x(x-24)+4(x-24)=0
(x+4)(x-24)=0
x = -4 or 24
(-4 is not possible because x is a positive integer)
Hence the number is 24

Answer 2

Let the integer be x
From the condition we get,
x^2 - 96 = 20x
=> x^2 - 20x- 96=0
=>x^2 + 4x - 24x - 96= 0
=> x(x + 4) -24(x + 4)=0
=>(x + 4)(x - 24)=0
Therefore x = -4 or 24
Since it can not be -4 it is 24