Question

Find three consecutive positive integers such that the sum of the squares of the first and second equals the square of the third.

Answer 1

3, 4 , 5

Answer 2

Can you please explain how and why?

Answer 3

no idea... i know those from trigonometry lol... sorry :/

Answer 4

I'm doing this lesson soon and I want to go into the classroom knowing, but thanks for the help

Answer 5

Well, first step is to represent your values :)
You have three consecutive positive integers, right?
so
x, x + 1, and x + 2 is a good way to represent those three
agree? :)

Answer 6

By the way, x - 2, x - 1 and x should work just fine :)

Answer 7

Maybe even x - 1, x, x + 1

It's your preference :)

Answer 8

so, once I have those, What would be my next step?

Answer 9

I shall quote the problem (and use x, x+1 and x+2, they're my preference, lol)
"the sum of the squares of the first and second equals the square of the third"

Does that give you an idea? :)

Answer 10

This is my first time doing this and it's so confusing. I am guessing that x,x would be the first two integers plus one?

Answer 11

Ok, I'll walk you through this :)
Your first integer is x
Your second integer is x + 1
Your third integer is x + 2

Now how can you express that last bit
(the sum of the squares of the first and second equals the square of the third)
in mathematical symbols? :)

Answer 12

X-1
X+1=2
X+2=3

So, the integers would be 1,2,3?

Answer 13

No, we don't know the values of these integers yet, all we know is that they are consecutive
(Hence, our second is just one more than the first and the third is just one more than the second)

and that the sum of the squares of the first two is equal to the square of the third :)
I'll continue on and explain along the way if you like :)

Answer 14

Yes, but I am having a hard time figuring out what exactly the squares are. Are they the Square roots?

Answer 15

No :)
The square of the first integer is x^2
The square of the second integer is (x + 1)^2

get it? :)

Answer 16

oh!

Answer 17

Can you do it from here? :)

Answer 18

Let me give it a shot, hold on.

Answer 19

The best I got was 3,4,5 but the subs of the squares of 3 and 4 equal to 21

Answer 20

no it isn't :) try 9 + 16 again :)

Answer 21

And I do hope you did get 3,4, and 5, not just mimicking ganeshie8 ;)

Answer 22

Oh, I made a mistake while adding them

Answer 23

So they would be 3,4,5

Answer 24

That's right, and that's exactly what @ganeshie8 said, but congratulations on getting them yourself ;)

Answer 25

Thank you for your time and patience with me, I'm basically new to all this stuff and its been so much lately