Question

The product of two consecutive even integers is 120. Find the two integers.

Answer 1

you know what does consecutive mean ?

Answer 2

Yes, I'm just too lazy to think right now lol

Answer 3

10*12

Answer 4

lol, ok
and they are even
so, if smaller integer is x
the larger integer will be x+2
do you get this ?

Answer 5

Thank you beautiful!! @Shay17 :)

Answer 6

yes, I get it.

Answer 7

yw

Answer 8

u still wanna know how to actually grt those ?

Answer 9

*get

Answer 10

My online work says I need two sets of numbers. a higher and lower set.

Answer 11

Yes, please because I dont think I'm completely done lol :/

Answer 12

thats right.

so, product is 120
x(x+2) = 120
got this ?
thats a quadratic
and i thinky ou know how to solve quadratics :)

Answer 13

ehh, do I reaaaally have to think right now? lol

Answer 14

if you want to learn and practice, yes.
anyways i would not give you the other set. i can make you find it out by yourself if you are willing to think :)

Answer 15

ugh, ok lol

Answer 16

\(x^2+2x =120 \\ x^2+2x-120 =0\)
know how to solve this quadratic?

Answer 17

uhh, yeah? lol

Answer 18

good
then tell me the 2 values of x you get.

Answer 19

-12 & 10 (Not gonna lie, I cheated, buuuuut I got the answers)

Answer 20

ok
so, x and x+2

when x= 10, x+2 =12, {10,12}
when x= -12, x+2 = -10, {-10,-12}

Answer 21

Ooooooh, I get it. Ok.

Answer 22

cool :)

Answer 23

Sooooo, what do I put for the different sets?

Answer 24

i just gave you 2 sets!
{10,12}
{-10,-12}
thats it!

Answer 25

higher one is {10,12}

Answer 26

Oooooooh ! lol ok, thank you! :)

Answer 27

\[(x)(x+2)=120\]
\(x\) is your 1st even integer; \(x+2\) is your 2nd even integer.
\[x^2 + 2x = 120\]
\[x^2 + 2x + 1 = 120 + 1\]
\[(x+1)(x+1) = 121\]
Now you see that the same number \(x+1\) multiplied by itself is 121. So, what is the square root of 121? It is 11. Since you know that \(x+1 = 11\), you know that \(x=10\), which is your first even integer. Now, the 2nd integer is \(x+2 = 10+2 = 12\).

Just so you know how to sold the quadratic without cheating. :)

Answer 28

solve*