4.Three times the square of a certain positive number exceeds six times the number by nine. Find the number:
2006-12-19 12:50:25 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
3*n^2=6*n+9
Divide both sides by 3:
n^2=2n+3
Set to zero:
n^2-2n-3=0
Factor:
(n-3)(n+1)=0
So n=3 or n=-1 but our solution must be positive so it's 3.
2006-12-19 12:55:12 · answer #1 · answered by Professor Maddie 4 · 0⤊ 0⤋
Turn the words into numbers:
3 * x^2 = 6x + 9
3x^2 = 6x + 9
3x^2 - 6x - 9 = 0
Now solve by factoring.
3( x^2 - 2x - 3) = 0
x^2 - 2x - 3 = 0
(x - 3)(x + 1) = 0
Solve this by setting each factor to zero.
x - 3 = 0
x = 3
x + 1 = 0
x = -1.
The answer is 3 and -1. But go back to the question. See how it says "a certain POSITIVE number..." ? Since the answer has to be positive, we can eliminate -1.
The answer is 3. Hope that helps!
2006-12-19 12:59:40 · answer #2 · answered by teekshi33 4 · 0⤊ 0⤋
Let x represent the positive number.
3x^2 - 6x = 9
3x^2 - 6x - 9 =0
x^2 - 2x - 3= 0
(x - 3)(x +1) = 0
x - 3 = 0 or x + 1 = 0
x = 3 or x = -1
Since x must be positive, x = -1 is inadmissible.
Therefore, the number is 3.
2006-12-19 12:55:44 · answer #3 · answered by keely_66 3 · 0⤊ 0⤋
x is the number
Statement expressed algebraically:
3x^2 = 6x + 9
Simplifying (divide both sides by 3)
x^2 = 2x + 3
moving all terms to the left side:
x^2 - 2x - 3
Converting to factors:
(x - 3) (x + 1)
So, x is +3 or -1
Since the question is asking about a positive number, the only answer is +3
2006-12-19 12:56:52 · answer #4 · answered by Renaud 3 · 0⤊ 0⤋
Put that in equation form:
3 x^2 = 6x + 9
If you rearrange, you have
3x^2 - 6x - 9=0
Then you solve the quadratic. There are 2 roots: 3 and -1. But it was stated the number is positive, so...
2006-12-19 12:54:19 · answer #5 · answered by Vincent G 7 · 0⤊ 0⤋
Let the number be 'x'.
3x^2 = 6x + 9
==> 3x^2 - 6x - 9 = 0
==> x^2 - 2x - 3 = 0
==> (x - 3)(x + 1) = 0
==> x = 3, or (-1)
???
Is this what you mean? Hope this helps.
2006-12-19 12:56:48 · answer #6 · answered by Anonymous · 0⤊ 0⤋
3 times thesquare of the no is 3x^2
six times the no=6x
the equation
3x^2=6x+9
3x^2-6x-9=0
3(x^2-2x-3)=0
3(x-3)(x+1)=0
so x=3 or -1
since the q says +ve no the answer is 3
2006-12-19 12:58:34 · answer #7 · answered by raj 7 · 0⤊ 0⤋
3x^2 > 6*9
3x^2 > 48
x^2 > 16
x > 4
yeah. i want to know how they get 3 too. or i misunderstood the question.
2006-12-19 12:58:15 · answer #8 · answered by Mr.Math 1 · 0⤊ 0⤋
it is 3.
3x9(square of 3)=27
6x3=18
27-18=9
Why? What did you get?
2006-12-19 13:00:44 · answer #9 · answered by Anonymous · 0⤊ 0⤋