Question #14

Question

I am thinking of three consecutive integers. The square of the largest one equals the sum of the squares of the other two. FInd the integers. 

Answer 1

x-1, x, and x+1 are the 3 consecutive integers

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

x^2+2x+1=x^2+x^2-2x+1

cancel one x^2 from both sides and cancel the number 1 from both sides to get...

2x=x^2-2x

x^2-2x-2x=0

x^2-4x=0

x(x-4)=0

x-4=0

x=4

x-1=3

x+1=5

3, 4, and 5 make up one answer

x=0

x-1=-1

x+1=1

-1, 0, and 1 make up another solution

also, look at consecutive squares:

1, 4, 9, 16, 25, 36, ...

9+16=25 (3^2+4^2=5^2)

you might have learned this in geometry; if the hypotenuse is 5 and the legs of a right triangle are 3 and 4, or if the three sides are multiples of 3, 4, and 5 you have what is called a "3-4-5" right triangle