Question

Find four numbers in app whose sum is 6 and sum of whose squares is 14

Answer 1

x - 1, x, x + 1,  x+2

x - 1 + x + x + y + x+2 = 6

4x = 4

x = 1

(x-1)² + (x)² + (x+1)² + (x+2)² = 14

(1-1)² + 1² + (1+1)² + (1+2)² = 14

0 + 1 + 4 + 9 = 14

numbers 0,1, 2, 3

Answer 2

let four number =a+3d,a+d ,a-3d,a-d

sum of four number =6
(a+3d)+(a+d)+(a-3d)+(a-d)=6
4a=6
a=3/2

square of sum of number =14
${(a + 3d)}^{2} + {(a + d)}^{2} + {(a - 3d)}^{2} + {(a - d)}^{2} = 14$
${a }^{2} + {9d}^{2} + 6ad+ {a }^{2} + {d}^{2} + 2ad + {a}^{2} + {9d}^{2} - 6ad + {a}^{2} + {d}^{2} - 2ad = 14$
$4 {a}^{2} + 20 {d}^{2} = 14$
put value of a in this equation
$4 \times {(3 \div 2)}^{2} + 20 {d}^{2} = 14$
$d = 1 \div 2$

put the value of a and d in letted number