another math question.... i've attempted it but im horrible.?

1st integer—x:

x(x + 1) = x + x + 1 + 11

x² + x = 2x + 12

x² - 1/2x = 12 + (- 1/2)²

x² - 1/2x = 48/4 + 1/4

(x - 1/2)² = 49/4

x - 1/2 = 7/2

x = 8/2 or 4

2nd integer:

= 4 + 1

= 5

Answer: 4 and 5 are the integers.

Let x be the first positive integer

then x+1 is the second

x(x+1)= x +(x+1) + 11, the right side is the product of consecutive positive integers, the left side is the sum of the positive integers plus 11

x^2 + x = 2x + 12

x^2 -x - 12 = 0

factor

(x-4)(x+3) = 0

x - 4 = 0 so x = 4

x + 3 = 0 so x would be -3 but you are dealing with positive integers so -3 is not an answer

the integers are 4, and 5 the product is 20 and the sum is 9 and the product is indeed 11 more than the sum

let me break it down for you

the product -- this means we're talking about multiplying numbers together

of two -- well that makes it easy, there's only two numbers to multiply

consecutive -- the numbers are in order as according to...

positive integers -- yes, it's spelled i-n-t-e-g-e-r-s, no R in the middle. positive means the numbers are greater than zero, integers are whole numbers. so "two consecutive positive integers" means a positive integer and the very next one in counting order. for example, 1 and 2, or maybe 2 and 3, or perhaps 3 and 4. well, we shall find out. note that if we subtract the first number from the second number we always get 1. so if we let x represent the smaller number, then we can represent the next consecutive integer after x as x+1.

alright, I think we can start taking bigger steps

the product...is 11 more than their sum

well the product of x and x+1 is simply x(x+1)

their sum means we add them together: x + x+1, which simplifies to 2x+1

if the product is more (11 more in fact) than the sum, that means it is a bigger number. so if we start with their sum, how do we make that a bigger number, specifically a bigger number that is 11 more? seems painfully obvious, doesn't it? we just add 11 to that sum. so now we have an equation.

product = sum + 11, which is

x(x+1) = 2x + 1 + 11

let's perform the multiplication indicated on the left, and simplify the right

x^2 + x = 2x + 12

now subtract what's on the right from both sides

x^2 - x -12 = 0

I think we can factor

(x - 4)(x + 3) = 0

if two numbers multiplied together equal zero, then one of them must be zero

so if x-4=0, then x=4

and if x+3=0, then x=-3

hence we have two possible solutions: x=4, x=-3

but the problem said we were looking for positive integers.

therefore x=4 is what we want. now remember x was the first integer. what was the second one? none other than x+1, which in this case is 4+1=5.

now we are finally done. 4 and 5 are the numbers we sought.

Let x be the first integer

x + 1 will be the second integer

(x)(x+1) = x+x+1+11 (add 11 to this side because the product is 11 more, so to make this an equation we must make both sides equal)

x^2+x = 2x+12

x^2-x-12 = 0 (now we must factor)

(x-4)(x+3) = 0

x = -3, 4

Now we go back to our original equation x values and plug -3 and 4 in for them.

For x = -3

First Integer = -3

Second Integer = (-3) + 1 = -2

We know -3 and -2 work because there product (6) is 11 more than their sum (-5).

For x = 4

First Integer = 4

Second Integer = (4) + 1 = 5

We know 4 and 5 work because there product (20) is 11 more than their sum (9).

So you have two sets of integers (-3 and -2) and (4 and 5).

Let the first integer = x. Then the other integer is x + 1...

(x)(x + 1) = x + (x + 1) + 11

x^2 + x = 2x + 12

x^2 - x - 12 = 0

(x - 4)(x + 3) = 0

Therefore, x = 4 or -3. As we are told the integers are positive, just take x = 4. Therefore, x + 1 = 4 + 1 = 5.

The two consecutive integers are 4 and 5.

4 and 5

4 and 5

4 and 5

Let the 2 consecutive positive integers be n , n+1:

n(n+1) = 11 + n + (n+1) = 12 + 2n

n^2 -n -12 = 0

(n-4)(n+3) = 0

n = 4, n = -3 .

n = -3 is dropped since we require positive integers.

So, the answer is 4 and 5

Product- The answer to a multiplication problem.

Consecutive - In a row.

Positive - 1,2,3,4,5......

Integers- a set of whole numbers and there opposites. -3,-2,-1,0,1,2,3.

Sum- Answer ot an addition problem

lets start at the beginning

1 x 2 = 3

1 + 2= 3...

So its not 1 & 2.

2&3.

2 x 3 = 6

2 +3 = 5

nope.

3 & 4.

3 x 4 = 12

3 + 4 = 7

nope.

4 & 5.

4 x 5 = 20

4 + 5 = 9

20 -9 = 11

Yes!

So ur answer is 4 & 5

4 x 5 = 20

then 5 + 4 = 9

20 - 9 = 11

:D

-xoxo

Let x be the first number so x +1 is the number after it

x(x + 1) = x + (x + 1) + 11

x^2 + x = 2x +12

x^2 + x - 2x - 12 = 0

x^2 - x - 12 = 0

(x - 4)(x + 3) = 0

x = 4, -3

Since it can only be a positive number it is 4 and 5