SOLUTION: find three numbers in arithmetic progression whose sum is 21 and whose product is 180

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

RELATED QUESTIONS
find three numbers in arithmetic progression whose sum is 21 and whose product is... (answered by solver91311)
Find three numbers in arithmetic progression whose sum and product are six and six... (answered by ikleyn)
find three numbers in geometric progression whose sum is 19 and product is... (answered by ramkikk66)
find three numbers in geometric progression whose sum is 19 and product is... (answered by ramkikk66)
find the three numbers in an arithmetic progression whose sum is 48 and the sum of their... (answered by ikleyn)
Find 3 numbers in the geometrical progression whose sum is 28 and whose product is... (answered by ikleyn)
Find three numbers in geometric progression whose sum is 21 and sum of their squares is... (answered by texttutoring)
Pls Help me with this question urgently,thanks. Find the three numbers in a... (answered by Edwin McCravy)
Find 3 number in the geometrical progression whose sum is 28 and whose product is... (answered by swincher4391,Alan3354)