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10 answers

n^2 + [(n + 1)^2] = 85
n^2 + n^2 + 2n + 1 = 85
2n^2 + 2n + 1 = 85
2n^2 + 2n = 84
n^2 + n = 42
n^2 + n - 42 = 0
(n - 6)(n + 7) = 0
n=6, or n=-7

Since the question specified positive integers, the answer is n=6, n+1=7.

2006-07-04 06:05:07 · answer #1 · answered by violet 5 · 0 0

Let x be an integer. x+1 would be the next consecutive integer.

x^2 (sorry about the limitations of the keyboard) is the square of the first integer, while (x+1)^2 would be the square of the second.

x^2 + (x+1)^2 = 85
x^2 + (x^2 +2x +1) = 85 (expanded)
2x^2 + 2x +1 = 85 (combined)
2x^2 + 2x -84 = 0 (subtracted 85 from each side)
x^2 + x - 42 = 0 (divide each side by two)
(x +7) (x-6) = 0 (factored)
Therefore, either x+7=0 or x-6=0.

x=-7 or x=6

But the question specified positive integers; therefore, x=6; the solution is 6 and 7.

2006-07-04 06:07:32 · answer #2 · answered by flyersbiblepreacher 4 · 0 0

Consecutive numbers are like 2 and 3 or 4 and 5

Try this:
4^2 =16
5^2 =25

Add: 41

Try the next two:

5^2 =25
6^2 =36

Add: 61

6^2 =36
7^2 =49

Add: 85

2006-07-04 14:40:28 · answer #3 · answered by Anonymous · 0 0

The way I would do it is to find all the squares less than 85, and then find out which ones add up. Or you could add up consecutive positive integers beginning with 1 and 2 and work your way up.

2006-07-04 10:01:28 · answer #4 · answered by Kevin F 3 · 0 0

Open a worksheet in Excel.
Put the numbers 1 to 10 in column A (cells A1 to A10)
Put +A1*A1 into cell B1
Copy B1 to cells B2 to B10
Put +B1+B2 into cell C1
Copy C1 to cells C2 to C9
Look down column C until you find 85
The A cell in that row will show 6, and the B cell 36
The A cell in the next row will show 7, and the B cell 49
36 + 49 = 85, so the integers are 6 and 7.

2006-07-04 06:15:51 · answer #5 · answered by mikeoxley242 5 · 0 0

x^2 + ( x+1)^2 = 85

x^2 + x^2 + 2X + 1 = 85

x^2 + x^2 + 2x +1 -85 =0

2x^2 + 2x - 84 = 0

(x-6 )(x+7) = 0

x= 6 or -7 (rejected)

two consecutive positive integers are 6 and 7

if not understand mail me
frankie_adam_li@yahoo.com.hk

2006-07-04 06:13:25 · answer #6 · answered by Kellogg 3 · 0 0

suppose the no. b x and x+1....coz they r consecutive
u r given tht
x^2 +(x+1)^2=85
x^2+x^2+2x+1=85
2x^2+2x=84
2x(x+1)=84
x^2+x=42
x^2+x-42=0
x(x+7)-6(x+7)=0
(x+7)(x-6)=0
solve this
u would get 7 & 6 answer

2006-07-04 06:12:10 · answer #7 · answered by Gaurab N 3 · 0 0

n2 + (n-1)2=85

n2+n2-2n+1=85
2n2-2n=84
2n2-2n-84=0
n2-n-42=0 1 -7 6
1 6 -7
-1

(n-7)(n+6) n=7 n=-6
n=7 n-1=6

(7)2*(6)2=85

your numers is 7 & 6

2006-07-04 06:10:39 · answer #8 · answered by E_Derevko 2 · 0 0

square route of x plus the square route of x plus one = 85 ,now you just do common algebra

2006-07-04 06:05:13 · answer #9 · answered by cam 1 · 0 0

Kids today are so lucky.

When I was in school, we actually had to do our own homework.

2006-07-04 06:04:09 · answer #10 · answered by ratboy 7 · 0 0

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