HARD RIDDLE / ALGEBRAIC PROBLEM!!? NEED HELP 10 pts!?

Question

hi
Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17

how do i do this!!

lol okay i found out that y =13.2801098892805

Answer 1

The first two answers have not read the question carefully enough. The 2 equations to be solved should be:
x - y = 12
xy = 17

From the first equation we obtain y = x - 12
Substituting into the second equation we obtain
x(x - 12) = 17
x² - 12x - 17 = 0

Solving the quadratic equation we arrive at
x = -1.28 or x = 13.28

Correspondingly we calculate y as
y = -1.28 - 12 = -13.28 or
y = 13.28 - 12 = 1.28

Answer 2

Let the two numbers be x and y.

x - y = 12
xy = 17

To do this, use substitution. x - y = 12 means x = 12 + y. Plugging this into the second equation,

(12 + y)y = 17

Expand the left hand side.

12y + y^2 = 17

Move everything to the left hand side.

y^2 + 12y - 17 = 0

We have no choice but to use the quadratic formula to obtain the numbers. They're not going to be clean numbers.

y = [-b ± √(b² - 4ac)]/(2a)

y = [-12 ± √(144 - 4(-17))] / 2

y = [-12 ± √(144 + 68)] / 2

y = [-12 ± √(212)] / 2

y = [-12 ± 2√(53)] / 2

y = -6 ± √(53)

We have two values for y; y = -6 + √(53) and y = -6 - √(53).

To obtain the corresponding x value, remember that
x = 12 + y.

When y = -6 + √(53), x = 12 + -6 + √(53) = 6 + √(53).
When y = -6 - √(53), x = 12 + -6 - √(53) = 6 - √(53).

Since we are talking about the same two numbers either way, we have one solution.

x = -6 + √(53) , y = -6 - √(53)

Answer 3

make two equations. say x is the first number, and y is the second.
x - y = 12
x + y = 17

now you can either solve by substitution or elimination.
substitution:
x - y = 12 is the same as x = y + 12. therefore, you can replace the 'x' in the second equation with 'y + 12'.
(y + 12) + y = 17
2y = 5
y = 5/2 = 2.5
then plug y in either of the two equations to find x.
x - 2.5 = 12
x = 12 + 2.5
x = 14.5

elimination: set this up as an addition problem, with one equation over the other.
.. x - y = 12
+ x + y = 17
this eliminates the y, because -y + y = 0. therefore you now have
2x = 29
x = 14.5
then plug x in to find y.
14.5 - y = 12
2.5 = y

both ways will work. you end up with:
x = 14.5
y = 2.5

i hope i helped!

Answer 4

A - B = 12
A * B = 17

A = (12 + B)
Substitute this for A
(12+B) * B = 17
12B + B^2 = 17
1 B^2 + 12 B - 17 = 0

Just plug a = 1, b=12, and c = -17 into your quadratic equation:

x=-b/2a±sqrt(b²-4ac)/2a

and you have your answer.

Answer 5

A-B = 12 or B-A = 12
AB = 17
So A = 17/B or B = 17/A
So A - (17/A) = 12 or B - (17/B) = 12
To remove some of the ambiguity here you can assign A as the larger number, then you have
A-B = 12, AB = 17, and A - (17/A) = 12
Then you can solve for A:
A^2 - 12A - 17 = 0
plug it into the quad formula, as it does not factor

Answer 6

two numbers....x and y.

Difference of the two numbers ----> x-y=12
solve for y y = x-12
The product of two numbers is 17 xy= 17

Substitute the x with the answer of the first problem....

x(x-12)= 17 use PEMDAS (order of ops to distribute functions)

X^2 - 12x - 17 = 0
a b c

Plug numbers into the quadratic equation according to the coefficients (include negative signs when applicable) and go with the answer that makes most sense...
plug it into the first equation to check for true answer...answer should cancel equation to zero...

Answer 7

Let x and y b ethe two numbers and x>y
x-y=12
xy=17
y=17/x
x-17/x=12
x^2-12x-17=0
x=(12+sqrt(12^2+4*17))/2;(12-sqrt(12^2+4*17))/2
x=6+sqrt(53); 6-sqrt(53)

Answer 8

make two equations. say x is the first number, and y is the second.
x - y = 12
x + y = 17

now you can either solve by substitution or elimination.
substitution:
x - y = 12 is the same as x = y + 12. therefore, you can replace the 'x' in the second equation with 'y + 12'.
(y + 12) + y = 17
2y = 5
y = 5/2
then plug y in either of the two equations to find x.
x - (5/2) = 12
x = 12 + (5/2)
x = 14.5

Answer 9

x-y=12 (1)
x*y=17=>x=17/y(2)
(2)->(1)
17/y-y=12
17-y^2-12y=0
y^2+12y-17=0
y1,2=[ -12+,-sqrt(144+68)]/2
y1,2==[ -12+,-2sqrt53]/2
y1,2=-6+,-sqrt53
x1,2=-6-,+sqrt53