- #1

liz

- 23

- 0

(im presuming n^2 means n squared)

prove the following result: "a traingle with sides that can be written in the form n^2+1, n^2-1, and 2n (where n>1) is right angled.

show, by means of a counter example, that the converse is false.

this q was taken from the back of the book "the curious incedent of the dog in the night-time" and there was a full proof but i don't understand some of it.

it start by exmplaining we need to prove which side is the longest by doing:

n^2+1 - 2n = (n-1)^2

if n>1 then (n-1)^2 >0

therefore n^2+1 > 2n

similarily (n^2+1) - (n^2-1) = 2

therefore n^2+1 > n^2-1

so n^2+1 > n^2-1.

the rest is worked out using pythagoras but then the converse bit has completely lost me.

if anyone would like to explain, then i would be very grateful. thanks!