Question 192689: find three numbers in arithmetic progression whose sum is 21 and whose product is 180
Found 2 solutions by stanbon, RAY100:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1st: x
2nd: x + d
3rd: x = 2d
x + x + d + x + 2d = 21
3x+3d = 21
x + d = 7
----------------
x(x+d)(x+2d) = 180
x(7)(x+2d) = 180
7x^2 + 14xd - 180 = 0
----------------------------
Solve the system using substitution: d = 7-x
7x^2 + 14x(7-x) - 180 = 0
7x^2 + 98x - 14x^2 - 180 = 0
-7x^2 + 98x - 180 = 0
x = 11.83 or x = 2.174..
-----------------
Find d using d = 7-x
==============================
Cheers,
Stan H.
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website! Let arithmetic sequence be x, x+d, x+2d. sum is 3x +3d=21, or x+d=7 (KEY)
multiply (x) (x+d) (x+2d) = 180
x^3+3dx^2+2d^2x=180 (KEY)
but x+d=7, therefore x=7-d (KEY)
substitution and simplyfing
-7d^2+163=0
d=4.8255 ANSWER
but x=7-d, x=7-4.8255 , x=2.1744 ANSWER
set is 2.1744, 7, 11.8254 SUMMARY ANSWER
check
2.1744 +(2.1744+4.8255)+(2.1744+4.8255+4.8255)=21 ok
2.1744 * (2.1744+4.8255)*(2.1744+4.8255+4.8255) = 180 ok
|
|
|
