SOLUTION: Find three numbers in A.P. such that their sum is 27 and the sum of their squares is 341..

Question 922109: Find three numbers in A.P. such that their sum is 27 and the sum of their squares is 341..
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find three numbers in A.P. such that their sum is 27 and the sum of their squares is 341..
======
a + (a+d) + (a+2d) = 27
a^2 + (a+d)^2 + (a+2d)^2 = 341
-------
3a + 3d = 27
-----
a + d = 9
a^2 + 9^2 + (9+d)^2 = 341
------
a + d = 9
a^2 + 9^2 + 9^2 + 18d + d^2 = 341
a^2 +18d + 162 + d^2 = 341
-------------------------
a + d = 9
a^2 + 18d + d^2 = 179
-----
a = 9-d
------
(9-d)^2 + 18d + d^2 = 179
81-18d+d^2 + 18d + d^2 = 179
81 + 2d^2 = 179
2d^2 = 98
d^2 = 49
d = 7
Then a = 2
---------------------
Checking::
Sum = 27 ??
2 + (2+7) + (2+14) = 6 + 21 = 27
2^2 + 9^2 + 16^2 = 341
============================
Cheers,
Stan H.
--------------------

RELATED QUESTIONS
find three numbers in continued proportion such that their sum is 14 and sum of their... (answered by ankor@dixie-net.com)

Find three numbers in continued proportion such that their sum is 14 and sum of their... (answered by Edwin McCravy)

Find the three numbers in an AP such that their sum is 27 and their product is... (answered by ikleyn)

find two numbers such that their sum multiplied by the sum of their squares is 5500, and... (answered by oscargut)

Three numbers are in AP such that their sum is 18 and sum of their squares is 158 the... (answered by ikleyn)

Find 2 positive numbers whose sum is 20 such that the sum of their squares is a... (answered by Alan3354)

Find two numbers such that their sum multiplied by the sum of their squares is 65, and... (answered by mananth)

the sum of three numbers in G.p is 19 and the sum of their squares is 133 find the... (answered by ankor@dixie-net.com)