In the equation n+5−−−−√−n−10−−−−−√=1, the value of n is

Question

specek18 · Answer

attachment

specek18 · Answer

@satellite73

anonymous · Answer

probably 11

anonymous · Answer

you can solve this the math teacher way, but it is kind of a pain in the neck
it is easier to guess

specek18 · Answer

that was my guess too, but i have a feeling it should be way more complicated. lol

anonymous · Answer

here is the deal 
if $n+5$ and $n-10$ are both perfect squares, then there are not a lot of choices for $n$

specek18 · Answer

okay...i went with 11 because i thought it'd equal 1 but i didnt enter it,...don't really know so does any one else have an opinion or idea?

anonymous · Answer

i focussed on $n-10$ and though if $n=11$ then $n-10=1,n+5=16$ both squares 
but $4-1=3$ so 11 is not right, lets move to the next possibility

anonymous · Answer

i it is not 11, lets try again

jhannybean · Answer

$$\sqrt{n-5} -\sqrt{n-10} = 1$$$$\sqrt{n-10} = \sqrt{n-5}-1$$$$n-10=n-5+2\sqrt{n-5}+1\ ...$$

jhannybean · Answer

Can't solve it in that method?

anonymous · Answer

think you might have made a small mistake

anonymous · Answer

$$n-10=n-5\color{red}-2\sqrt{n-5}+1$$

specek18 · Answer

i'm so confused...lol

jhannybean · Answer

Ah yeah the negative.

perl · Answer

you can solve the equation by first adding `sqrt(n-10` to both sides
then squaring both sides of the equation

anonymous · Answer

i still like the guess method
how can $n-10$ and $n+5$ both be perfect squares?

anonymous · Answer

Ik ur not supposed to give the answer but walk them through and help them but its 59

anonymous · Answer

11 works 
there are not that many squares around 
16 makes n = 26
25 makes n = 35
36 makes n = 46
49 makes n = 59 bingo, both 49 and 64 are perfect squares!

specek18 · Answer

this is insane. lol so there can be more than one answer but it's not multiple choice???

jhannybean · Answer

$$n-10=n-5-2\sqrt{n-5}+1$$$$n-10=n-2\sqrt{n-5}-4$$$$6=-2\sqrt{n-5}$$$$-3=\sqrt{n-5}$$$$9=n-5$$Etc.

anonymous · Answer

there  is  and answer, it is 59

anonymous · Answer

*one answer

specek18 · Answer

okay...i wrote down what @Jhannybean said and it's making a little more sense....thank you to everyone for helping me out and dealing with me!!! only 3 more questions...haha

jhannybean · Answer

@satellite73 can you elaborate on your guess and check method? I'd like to learn this.

specek18 · Answer

i understood what you did @Jhannybean but i just sort of accepted that @satellite73 is a genius. lol i have no clue what she did either!

jhannybean · Answer

There's always time to learn new techniques :)

specek18 · Answer

i was able to do the next two by myself but i have one left....

jhannybean · Answer

post it in a new question :)