Help please!!!!?

Question

The product of two consecutive positive even integers is 288. Set up an equation and solve to find the integers.

Answer 1

Hi,

If x = 1st even integer, then the next larger one is 2 more than the previous even integer, so it is x + 2. Their product would come from multiplying them together. This gives the equation:

x(x + 2) = 288
x² + 2x = 288
x² + 2x - 288 = 0
(x + 18)(x - 16) = 0
Solving each factor:

x + 18 = 0
x = -18
Discard this answer because it is not positive as the problem required.

x - 16 = 0
x = 16
If x = 16, them x + 2 = 18. So the 2 consecutive even integers that have a product of 288 are 16 and 18.

I hope that helps!! :-)

Answer 2

2 consecutive positive even integers refers to 2 numbers:
x and (x+2)
x2+2x=288
x2+2x-288=0

quadratic formula:
x=(-2 (+/-) sqrt(4 - 4(1)(-288))) /(2) (that's a mess, sorry)
x=-1(+/-) sqrt(1+288)
x= -1 (+/-) 17
x can be either 16 or -18. The condition was that the integers were positive, so x must be 16. Therefore the two integers are 16 and 18.

Answer 3

16*18

first list all integers of 288: 1, 2, 4, 6, 8, 12, 16, 18, 24....

there you go 16 and 18.. 2 consecutive even integers

Answer 4

Let x = the first integer
Then x +2 = the other integer
x(x+2) = product = 288
x^2+2x-288 = 0
(x+18)(x-16) = 0
x = 16

The numbers are 16 and 18

Answer 5

Let integers be 2x and 2x + 2
2x (2x + 2) = 288
4x² + 4x - 288 = 0
x² + x - 72 = 0
(x + 9) (x - 8) = 0
x = 8 is acceptable value.
Numbers are 16 and 18

Answer 6

Let x be the first integer. The next positive even integer would be x+2.
So, x(x+2)=288
x²+2x=288
x²+2x-288=0
(x+18)(x-16)=0
x=-18,16
x can not be 18 because it is not positive.
16,18

Answer 7

x*(x+2)=288
x^2 + 2x - 288 = 0
(x + 18) (x - 16) = 0

x = -18 or +16

Since you want the positive consecutive integers, you know that -18 can't be x.

The answer is 16 and 18.

Answer 8

y = x + 2

xy = 288
x(x + 2) = 288
x² + 2x = 288
x² + 2x - 288 = 0
(x + 18)(x - 16) = 0

x = 16 or -18

Since you care about "positive consecutive even integers", the answer is:

x = 16
y = 18

Answer 9

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