Logic and methodology would be appreciated.
2006-10-22 10:21:17 · 11 answers · asked by sattarsoul 2 in Science & Mathematics ➔ Mathematics
(1/2)x + (1/4)x^2 = 6. Let's multiply through by 4 so we don't have to deal with fractions. 4 is the smallest number that will remove the fractions, based on the 1/4.
2x + x^2 = 24. This is developing into a quadratic equation, let's rearrange it: 2x + x^2 - 24 = 0, then x^2 + 2x - 24 = 0. Find two numbers whose sum is 2 (2x), and product is -24. I get -4 and 6. These are the linear factors: (x - 4)(x + 6) = 0.
The solutions are 4 and -6, but the question asked for a positive number, so the answer is 4.
2006-10-22 10:30:52 · answer #1 · answered by Action 4 · 0⤊ 0⤋
4
2006-10-22 10:28:33 · answer #2 · answered by briley4242 3 · 0⤊ 0⤋
the number is 4 because 1/2 of 4= 2 plus 4 squared is 16 1/4 of 16 is 4 4plus 2= 6
2006-10-22 10:27:02 · answer #3 · answered by postalbro. 2 · 0⤊ 0⤋
Re-writing this in formula:
Let the "positive number" be "X"
(X/2 + X(squared)/4) = 6
Is this correct??
If so..
Then start by converting the denominators within the LEFT side of the equation:
So 4X + 2X(squared) = 48
Simplify this (dividing everything by 2): 2X + X(squared) = 24
So X(squared = (24 - 2X)
By simply trail and error now.. you can easily deduce that X must be a number between 3 and 4.. it is actually 4
The answer is X or the positive number you seek is 4
2006-10-22 10:36:19 · answer #4 · answered by Anonymous · 0⤊ 0⤋
1/2n + 1/4n^2 = 6
Subtract 6 from each side to set up a quadratic equation in standard form
1/4 n^2 + 1/2n - 6 = 0
Use the Quadratic Formula to figure out what n is.
n = 4, -6. Due to the conditions of the problem, eliminate the negative answer.
The answer is 4.
2006-10-22 10:31:13 · answer #5 · answered by Bentnalboy 3 · 0⤊ 0⤋
This is a quadratic equation.
1/2x + 1/4X^2 = 6 can be rearranged in two steps to look like a more conventional quadratic, by subtracting six from both sides, then multiplying both sides by four to look like this.
x^2 +2x -24 = 0
You can then factor to get (x+6)(x-4) = 0. That leaves you with solutions of -6, or 4.
Your answer is the positive solution, which is 4.
2006-10-22 10:30:15 · answer #6 · answered by metatron 4 · 1⤊ 0⤋
1/2 x + 1/4 x^2 = 6
Clearing fractions
2x + x^2 = 24
Setting = 0 and factoring:
x^2 + 2x -24 = 0
(x+6)(x-4) = 0
so x = 4
2006-10-22 10:29:19 · answer #7 · answered by MollyMAM 6 · 0⤊ 0⤋
(1/2)x + (1/4)x^2 = 6
2x + x^2 = 24
x^2 + 2x - 24 = 0
(x + 6)(x - 4) = 0
x = -6 or 4
Since you wanted it positive, the answer is 4
2006-10-22 11:25:54 · answer #8 · answered by Sherman81 6 · 0⤊ 0⤋
1/2 x +n +1/4= 6
1/6 x n = 6
n=6 x 6
n = 36
2006-10-22 10:24:59 · answer #9 · answered by Anonymous · 0⤊ 1⤋
x/2 + x^2/4 =6
x^2+2x -24=0
factorizing and we get
x=4 and x= -6
since you said positive no.
thus x=4
2006-10-22 10:26:59 · answer #10 · answered by amit v 2 · 0⤊ 0⤋