Question

A number 15 is divided into 3 parts which are in Arithmetic Progression and the sum of their squares is 83 . What is the smallest part ?How to find it ? Plz help !

Answer 1

let the first part be x..
thus second part= 15-x
third part=15-x-x=15-2x
x^2 + (15-x)^2 + (15-2x)^2= 83

Answer 2

thanks !

Answer 3

no problem

Answer 4

but no real root for the equ if we do like this ?

Answer 5

whaaaaaaattttt... wait i'll solve it

Answer 6

ok

Answer 7

sorry the equation wont be formed like this wait ill tell u how to do it

Answer 8

ohok

Answer 9

15 is divided into three parts which are in arithmetic progression
this means the numbers are consecutive
let first part=x
second part=x+1
third part=x+2
thus the equations are formed simultaneously
1st equation: x+(x+1)+(x+2)=15
2nd equation: \[x ^{2}+(x+1)^{2}+(x+2)^{2}=83\]

solving 1st equation 3x+3=15
x=4
hopefully this is correct

Answer 10

is the sum of the numbers square is = 83.. Check it out once... @mohammad.arqum

Answer 11

isn't it right @praxer ?

Answer 12

see, x was found to be 4 so the numbers will be 4,5 and 6 ..... right?

but 4^2+5^2+6^2 = 77 not 83

Answer 13

yes but answer is same
i have done it in another way

Answer 14

hmm

Answer 15

same ques here too now !

Answer 16

...@mohammad.arqum it is 77 not 83... But according to the question it should be 83 ........right ?

Answer 17

ok then the equation should become the second one
\[x ^{2}+(x+1)^{2}+(x+2)^{2}=83\]

Answer 18

but hw can we say that the common difference is 1 ? d can be any other number too right ?

Answer 19

they are in arthemetic progressiom

Answer 20

Arithmetic progression does not necessarily mean they have to be consecutive, while 4, 5, and 6 are a arithmetic progression, so is 2, 4, 6,

Answer 21

mutherfckr

Answer 22

support @saravananr ...
@mohammad.arqum follow @radar. A.P can have any common difference.

Answer 23

@mohammad.arqum , why do u use foul language ?

Answer 24

okee back to the question

Answer 25

ok

Answer 26

so anyone know how to do em

Answer 27

not me !

Answer 28

wait

Answer 29

I haven't resolved this problem, and would love to see it solved for my own education.

Answer 30

yeah me too

Answer 31

\[x+(x+n)+(x+2n)=15\]
\[3x + 3n = 15\]
\[n=5-x\]

\[(x^2)+(x+n)^2+(x+2n)^2 = 83\]
\[(x^2)+(x+5-x)^2+(x+10-2x)^2 = 83\]
\[x^2+5^2+(10-x)^2=83\]

that should work I think

Answer 32

oh ! that's gr8 !

Answer 33

\[x^2+25+100-20x+x^2-83=0\]
\[2x^2-20x+42=0\]
\[x^2-10x+21=0\]

Answer 34

well i think it is best to solve the problem by the trail and error method

The answer is 3,5, and 7

try it out yourselves

Answer 35

Thanks a lot @AllTehMaffs

Answer 36

Here are some arithmetic that sum up to 15 (other than 4, 5, and 6)
2, 5, and 8
1, 5, and 9 squares add up to 93

Answer 37

How did I miss that one lol

Answer 38

i think you r process iz better and logical than mine (y) @AllTehMaffs

Answer 39

x=3 or 7 ! ?

Answer 40

so whats the answer then

Answer 41

It's 3 - even if the series is any fraction, 3*7>15

Answer 42

~the common ratio

Answer 43

the smallest part is three then
what about remaining two parts

Answer 44

Thanks @AllTehMaffs That seems to work.

Answer 45

plug into n=5-x

n=2

3,5,7

Answer 46

yeah thats cool... :)

Answer 47

3, 5, and 7 or 7, 5, 3

Answer 48

thanks a lot @AllTehMaffs

Answer 49

both are okeeee

Answer 50

Oh! that's true! I forgot that n could be negative :P

And welcome ^_^

Hooray maths!

Answer 51

YAY!

Answer 52

Glad this was worked, as I was beginning to get a headache.

Answer 53

EVERYBODY TRY THIS ONE:
http://openstudy.com/updates/52ac5794e4b0f72fdcf70305

Answer 54

if n is -ve , it won't work here ! so ans is as already said , 3,5,7