Question

Difference is 3 and sum of squares is 369 the number is

Answer 1

Let the numbers are x and ( x + 3 )

Given, sum of squares = 369

x^2 + ( x + 3 )^2 = 369

x^2 + x^2 + 3^2 + 2( 3 x ) = 369

x^2 + x^2 + 6x + 9 = 369

2x^2 + 6x - 369 + 9 = 0

2x^2 + 6x - 360 = 0

x^2 + 3x - 180 = 0

x^2 + ( 15 - 12 )x - 180 = 0

x^2 + 15x - 12x - 180 = 0

x( x + 15 ) - 12( x + 15 ) = 0

( x + 15 ) ( x - 12 ) = 0

x = - 15 or x = 12

Taking positive value, x = 12

Hence,

numbers are x = 12 and ( x + 3 )= ( 12 + 3 ) = 15

Answer 2

Let the first number be x and second number be y

Difference between number = 3

x - y = 3

y = x -3

again, sum of squares = 369

x² + y² = 369

x² + (x-3)² = 369

x² + x² + 9 -6x = 369

2x² - 6x - 360 = 0

x² - 3x - 180 = 0

x² - 15x + 12x - 180 = 0

x(x - 15) + 12(x - 15) = 0

(x + 12) (x - 15) = 0

x = -12

x = 15

if x = -12 , y = -15

if x = 15 , y = 12

Hence numbers are -12 and -15 or 12 and 15