Question

The Pattern is that (Leg 1) ^2= Leg 2+ Hyp. This only works if Leg 1 is an odd integer.
Prove that this is true for all odd integers.

Answer 1

i dont understand the question =/
yo myininaya :)

Answer 2

if Leg 1=2k+1, then
(Leg 1)^2=4k^2+4k+1
so we have
4k^2+4k+1=leg 2 +hyp
now we got to see if this is possible
when it says prove for all odd integers
does that mean leg 2 and hyp are odd integers?
....
hey joe

Answer 3

no just leg 1 is an odd integer

Answer 4

one of either leg 2 or the hyp would need to be even, the other odd.

Answer 5

yes...

Answer 6

(3,4,5)
9=4+5
so leg 1 is also have to be the smallest leg i believe

Answer 7

because 16 doesn't equal 3+5

Answer 8

oh and 4 is not odd

Answer 9

but hows does this prove tru for all odd integers?

Answer 10

it doesn't
i was just thinking

Answer 11

oh ok

Answer 12

this isnt a true statement =/ check out this pythagorean triple

\[161^2+240^2=289^2\]
\[161^2=25921\]

Answer 13

You are looking at pythagorean triples i assume (since it was really never said). So they must satisfy the equation:
\[(leg_1)^2+(leg_2)^2=(hyp)^2\iff(leg)^2=(hyp)^2-(leg_2)^2\]\[\iff (leg_1)^2=(hyp+leg_2)(hyp-leg_2)\]
So, in order for your statement to be true, it must follow that:\[hyp-leg_2=1\]
,which is the case for the "smaller" pythagorean triples, but not the larger ones.