The product of two consecutive odd integers is 195. Find the integers.

Question

lgbasallote · Answer

hmm..well let's say the first integer is x so the next consecutive ODD integer would be x+2 yes?

so...

x(x+2) = 195 since the product of those two is 195

do you know what to do next?

anonymous · Answer

x^2+2=195?

anonymous · Answer

hell i would guess and check!

inkyvoyd · Answer

Find a rough estimate of the square root of 200.

anonymous · Answer

99 + 101 = 200 too big
95 + 97 = 192 too small 
try one more and i bet you get it

inkyvoyd · Answer

Then, guess and check. This isn't the way you are supposed to, but it is much faster.

inkyvoyd · Answer

sqrt(200) is about 14. So, try 13*15

inkyvoyd · Answer

Which is your answer.

anonymous · Answer

oh product, not sum
ok how about $13\times 15$

inkyvoyd · Answer

because, (14-1)(14+1)=14^2-1^1=196-1=195

anonymous · Answer

wow got it on the first try

anonymous · Answer

Lol thanks everyone

lgbasallote · Answer

lol @satellite73 =))))) nice strategy :P though it's product so it gets big...it gets slower hahaha

inkyvoyd · Answer

No, actually, two consectutive odd numbers is always easy

inkyvoyd · Answer

You can view it as (x)(x+2) where x is the smaller number
OR
you can view it as (x-1)(x+1), where x is the even number in between.

inkyvoyd · Answer

then, it's x^2-1=a
or, x=plusminus sqrt(1+a)

anonymous · Answer

well lets imagine that you want to solve an equation, and you write $x(x+2)=195$
the next thing you do is write $x^2+2x-195=0$ and then you think "can i find two numbers whose product is 195 that are two apart, which is exactly what the original problem asks!
so there is nothing gained by writing an equation

inkyvoyd · Answer

satellite, from that equation, all you have to do is complete the square; add 196 to both sides.

inkyvoyd · Answer

whenever I see x^2+2ax..., I always just add a^2 and go with it.

inkyvoyd · Answer

but seriously, note the difference between
x(x+2)
and (x+1)(x-1)
A little bit of thinking goes a long way...

anonymous · Answer

by complete the square i guess you could write 
$$x^2+2x=195$$
$$(x+1)^2=196$$ and then pray for a pefect square

anonymous · Answer

as luck would have it you get 14, but really i would for real guess and check. if you don't get it on the first try you are sure to get it on the second

inkyvoyd · Answer

Ok, how bout the product of an 2 integers, both odd, with one being 6 greater than the other? say the product is also 196...

inkyvoyd · Answer

*not 196, 187