help me please!?

Question

the sum of the squares of three consecutive odd integers is 875. Find the integers.

my teacher didnt show us how to do this so please someone help me. thanks!

Answer 1

If x is the middle odd number, the other odd numbers are (x-2) and (x+2). And you want to solve the equation:

(x-2)^2 + x^2 + (x+2)^2 = 875

That should be enough to get you started.

Answer 2

let the 3 nos be x, (x + 2), (x + 4)

Now,
x^2 + (x+2)^2 + (x+4)^2 = 875

x^2 + x^2 + 4x + 4 + x^2 + 8x + 16 = 875

3x^2 + 12x + 20 = 875

3x^2 + 12x - 855 = 0

Now, from the above we get,

a = 3, b = 12, c = -855

x = {-b +-sqrt[b^2 - (4*a*c)]}/2*a

x = 15

Hence the three consecutive odd numbers are as follows:

15, 17 & 19

Answer 3

Consecutive odd integers can be written as

x, x + 2, x + 4

The sum of their squares and the equation is

x^2 + (x + 2)^2 + (x + 4)^2 = 875
x^2 + x^2 + 4x + 4 + x^2 + 8x + 16 = 875
3x^2 + 12x + 20 = 875
3x^2 + 12x - 855 = 0
x^2 + 4x - 285 = 0
(x + 19)(x - 15) = 0

x = -19, x = 15

Discard negative root

The integers are 15, 17, 19

Answer 4

There are lots of interesting ways to approach this, but trial and error on a calculator works best.

Starting with 15 gives 875.

To solve this in general, you'll get a quadratic equation, something like x^2 + (x+2)^2 +(x+4)^2 = n, (in this proble n is 875), but a back of the envelop shows that starting at 20 is too high, which is why I think trying a few values is easier.

Answer 5

The answer is 15^2 + 17^2 + 19^2 = 875

How did I find them?

I assumed that the contribution of each squared numbers is about one third of the total rounded to 900: which is 300 whose square root is 17 approximately

I then cheched that 15^2 + 17^2 + 19^2 is indeed 875

Answer 6

3 consecutive odd integers, that means that if one is x, one is x+2 and the last one is x+4

Let's put that in equation:

x^2 + (x+2)^2 + (x+4)^2 = 875

Now, we expand:

x^2 + (x^2 + 4x + 4) + (x^2 + 8x + 16) = 875

and regroup

3 x^2 + 12 x + 20 = 875

3 x^2 + 12x - 855 = 0

this equation has 2 roots: -19 and 15.
So the consecutive odd integers are 15, 17 and 19
(or -19, -17 and -15 which are also odd integers...)

Answer 7

x^2+(x+2)^2+(x+4)^2=875
x^2+(x^2+4x+4)+(x^2+8x+16)=875
3x^2+12x+20=875
x=15

15 17 19 are the number

15^2 +17^2+19^2 = 875

also (-19)^2+(-17)^2+(-15)^2=875

Both sets of consecutive odd numbers give the answer

Answer 8

n^2+(n+2)^2+(n+4)^2=n^2+n^2+4n+4+n^2+8n+16=875
3n^2+12n+20=875
3n^2+12n-855=0
n=(-12+/-sqrt(144+4*3*855))/6
n=(-12+/-102)/6=-2+/-17
n=15
n=-19

3 numbers are 15,17,19

check
15^2+17^2+19^2=225+289+361=875

Answer 9

yip... he's right :P