Question

The sum of squares of three consecutive natural numbers is 770. Find the number .

Answer 1

Let the first number be x
second be x + 1
third number be x + 2


▪ The sum of their squares is 770


x² + ( x + 1 )² + ( x + 2 ) ² = 770

x² + x² + 1 + 2x + x² + 4 + 4x = 770

3x² + 5 + 6x = 770

3x² + 6x + 5 - 770 = 0

3x² + 6x - 765 = 0

( dividing by 3 )

x² + 2x - 255 = 0

x² - 17x + 15x - 255 = 0

x ( x - 17 ) + 15 ( x - 17 ) = 0

( x - 17 ) ( x + 15 ) = 0


* ( x - 17 ) = 0

x = 17


* ( x + 15 ) = 0

x = -15



If x = 17

then,

First number is 17

second number is x + 1
17 + 1 = 18

Third number is x + 2
17 + 2 = 19


If x = -15

First number is -15

Second number is x + 1

-15 + 1 = - 14

Third number is x + 2

-15 + 2 = -13