Question

Find two consecutive positive integers such that the sum of their squares is 841

Answer 1

Let x = 1st positive integer

Let x + 1 = 2nd positive integer

As give, their sum of squares is 841

`x^(2)+(x+1)^(2)=841`

`x^(2)+x^(2)+2x+1=841`

`2x^(2)+2x+1=841`

`2x^(2)+2x-840=0`

factor 2 out,
`x^(2)+x-420=0`

`x^(2)+21x-20x-420=0`

`x(x+21)-20(x+21)=0`

(x+21)(x-20)

This gives, x=20 and =-21 (neglect the negative value)

So, x = 20

x+1 = 21

So, the two numbers are : 20 and 21