if the sum of four numbers in A.P is24 and sum of thier squares is 164.then those numbers are
if the sum of four numbers in A.P is24 and sum of thier squares is 164.then those numbers are
Simran Bhatia , 11 Years ago
Grade 11
9 grade maths> progressions...
2 AnswersKaushik
Last Activity: 11 Years ago
they are 3,5,7,9
srinivas aytha
Last Activity: 11 Years ago
let the four no be a-3d,a-d,a+d,a+3d.
a-3d+a-d+a+d+a+3d=24 (given)
4a=24
a=6.
(a-3d)2+(a-d)2+(a+d)2+(a+3d)2=164 (given)
2(a2+9d2)+2(a2+d2)=164. since (a+b)2+(a-b)2=2(a2+b2)
2(2a2+10d2)=164.
2a2+10d2=164/2=82.
2(6)2+10d2=82.
10d2=10.
d=±1.
therefore four numbers are 3,5,7,9
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