Question

Find the 3 numbers in ap whose sum is 15 and the sum of there square is 83

Answer 1

Hey,

let three numbers be a,a-d,a+d

then a+a-d+a+d=15

therefore 3a=15

a=5

and a2+(a+d)2+(a-d)2=83

therefore 25+50+2d2=83

therefore 2d2=8

d=+2,d+-2

therefore numbers are 3,5,7 or 7,5,3.

HOPE IT HELPS YOU:-))

Answer 2

Let three number be a-d ,a,a+d .

$a - d + a + a + d = 15 \\ 3a = 15 \\ a = \frac{15}{3} \\ a = 5$

and

${( a - d) }^{2} + {a}^{2} + {(a + d)}^{2} = 83 \\ {a}^{2} + {d}^{2} - 2ad + {a}^{2} + {a}^{2} + {d}^{2} + 2ad = 83 \\ 3 {a}^{2} + 2 {d}^{2} = 83 \\ 3 \times {5}^{2} + 2 {d}^{2} = 83 \\ 2 {d}^{2} = 83 - 75 \\ {d}^{2} = \frac{8}{2} \\ d = + - 2$
so the three numbers are 3,5,7 or 7,3,5