what positive number when doubled, has a difference of 24 from its square?

Answer 1

Let x denote the number. Then, double it is 2x and its square is x^2. You want their difference to be 24. So, you want either


2x-24=x^2
or
2x+24=x^2.

You should veryify that the first equation has complex solutions,
x=1 +/- \sqrt{23} i

For the second equation,

2x+24=x^2
x^2-2x-24=0
(x-6)(x+4)=0

x=6 or x=-4

The positive number is 6.

Answer 2

6

Answer 3

Let x be the unknown number then,
Given

2x + 24 = x^2
or x^2 - 2x - 24 = 0
or x^2 +4x - 6x - 24 = 0
or x(x + 4) -6 (x+4) =0
or (x+4) (x - 6) = 0
Therefore, x = 6 or x = -4
Given that it is a positive number, we get x = 6

Verifying, we get 6*2 + 24 = 6^6
LHS = RHS
Proved

Answer 4

It is 6.

Solution:
Let x be the required number.
Then 2x + 24 = x^2
or x^2-2x-24 = 0
or x^2-6x+4x-24=0
or (x^2-6x) + (4x-24) = 0
or x(x-6) + 4(x-6) = 0
or (x+4) (x-6) = 0
Either x+4 = 0 which gives x = -4
Or x-6 = 0 which gives x = 6.
As we rquire only positive number, so the required number is 6.

Answer 5

6

6 x 2 = 12

6 x 6 = 36

36 - 12 = 24

Answer 6

Let the number be x
Given condition transforms in to the quadratic equation as under:
x^2-24=2x
x^2-2x-24=0
x={-b+/- (b^2-4ac)^1/2}/2a are the roots of eqution ax^2+bx+c=0
a=1,b=-2,c=-24
substituting we have
x={2+/-(4+96)^1/2}/2={2+/-10}/2=12/2 or-8/2=6,-4

Answer 7

Write it out as an equation X^2-2X = 24 (or 2X-X^2=24). This can then be rewritten as X^2-2X-24=0, which you should be able to solve.

When I used to be asked these questions and didn't need to supply proof, I would write a quick BASIC script and have the computer figure it out.

Answer 8

2x + 24 = x^2
0 = x^2 - 2x - 24
0 = (x + 4)(x - 6)

x = -4, 6 (only 6 meets the criteria expressed in the equation)

Answer 9

6

6•2=12
6^2=36

|6•2-6^2| = 36-12=24

Answer 10

x^2 - 2x = 24
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x = 6 or -4

Since you wanted a positive number

ANS : 6