Weird ? Help?

Question

The difference of the two numbers is 12. The product of the two numbers is 17.

Decimals included.

Any help would be awesome.

Thanks =)

Answer 1

your equations will be
x - y = 12 and xy = 17
you get a quadratic equation

x^2 + 12x - 17= 0

use the quadratic formula so solve for x.

you'll get

x = - 6 + sqrt(19) or
x = -6 - sqrt(19) //answer

Answer 2

Previous answer made a mistake as you can see by multiplying 19.5 X 7.5 = 146.25.
You need to set up 2 equations and then just use substitution:
X - Y = 12 and XY = 17. Work the substitution both ways and see which one is easier. (Just check the answers you get.)

I see that not many people can follow the quadratic formula through.
If X - Y = 12, then Y = X - 12
Substituting in XY = 17, we get X(X - 12) = 17
Multiplying we get x^2 - 12 X = 17 or X^2 - 12 X -17 = 0
a = 1, b= -12, c= -17
X = [-(-12) +/- Sqrt((-12)^2 - 4(1)(-17))]/2
X= [12 +/- Sqrt(144 - (4)(-17))]/2
X= [12 +/- Sqrt(144 + 68)]/2
X = [12 +/- Sqrt(212)]/2
X = [12 +/- 14.56...]/2
X= 6 +/- 7.28
X = 13.28 or -1.28
13.28 - 12 = Y or 1.28
X = 13.28, Y = 1.28
13.28 X 1.28 = 16.9984 which = 17 due to rounding.
13.28 - 1.28 = 12.

Therefore 13.28 and 1.28 are your numbers. Do each step carefully.

Answer 3

Since the difference of the two numbers is 12, we know that x - y = 12.
Since the PRODUCT of the numbers is 17 we know x*y = 17.

x - y = 12
x = y + 12

So, x*y = 17
(y+12)*y = 17
y^2 + 12y = 17
y^2 + 12y - 17 = 0

From here you use the quadratic formula to get the solutions.

(By the way the solutions are 6 +/- sqrt(53).)

Answer 4

With x being the larger of the two numbers x,y then your solutions sets are (x,y):

A) (6+sqrt53, -6+sqrt53) or B) (6-sqrt53, -6-sqrt53)

-----------------
Proof for A
6+sqrt53 - (-6+sqrt53) = 12
(6+sqrt53) (-6+sqrt53) = -36 + 53 = 17

Proof for B
(6-sqrt53) - ( -6-sqrt53) = 12
(6-sqrt53) ( -6-sqrt53) = -36 + 53 = 17
-----------------
You will need to CAREFULLY use the quadratic formula on:

Y^2 + 12Y -17 = 0 Then x = 12 + Y

Answer 5

x - y = 12
x*y= 17

x= 12+y
(12 + y)* y = 17
y^2 + 12y = 17
y^2 + 12y -17 = 0

Put that in the quadratic formula to get your answer.

Answer 6

x is one number
12-x is the other number
x(12-x) = 17
12x - x^2 = 17
x^2 -12x +17 =0
Quadratic formula or calculator
x = 10.36,1.64

Answer 7

x-y=12.....1
x=12+y.....2

x+y=17.....3

Put 2 into 3.
12+y+y=17
2y=15
y=7.5

x=12+7.5=19.5

So, the 2 numbers are 19.5 and 7.5.

I hope this helps. :)