Question

find 4 numbers in ap whose sum is 36and sum of the squares of the least and greatest is 234

Answer 1

x -3y, x-y, x+y, x+3y

x -3y + x- y + x+y + x+3y = 36

4x = 36

x = 9

least number x- 3y andgreatest number x+3y

(x-3y)² + (x+3y)² = 234

x² - 6xy + 9y² + x² + 6xy + 9y² = 234

2x² + 18y² = 234

x² + 9y² = 117

9y² = 117 - 81 = 36

y² = 4

y = 2

numbers

x - 3y = 9 - 6 = 3

x - y = 9 -2 = 7

x + y = 9 + 2 = 11

x + 3y = 9 + 6 = 15