Question

20 times a positive integer is more than its square by 96 then the positive integer is

Answer 1

Let the integer be x
20x +96 =x^2
x^2 - 20x - 96 = 0
x^2 - 12x - 8x - 96 =0
x ( x -12) - 8 ( x -12) = 0
(x - 12) ( x - 8) =0
x = 8 or 12
By verification, 12 is the answer

Answer 2

Let the Number be x,

According to the given informations,

20x =x² +96

0=x²-20x+96

0= x²-(12+8)x+96

0=x²-12x-8x +96

0=x(x-12)-8(x-12)

0=(x-12)(x-8)

x-12=0 Or x-8=0

x=12 Or x=8

Number Can be either 12 or 8

Now,

Verification, taking number as 8

20(8) should equal to 8²+96

160 should equal to (64+96)

160 should equal to 160

160=160

Hence, 8 is the number

taking number as 12

20(12) should equal to 12²+96

240 should equal to (144+96)

240=240

Hence, 12 is the number




Number can be 12 and 8



I hope this will help you




-by ABHAY