Grade 119 grade maths
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
2 Answers
Kaushik
they are 3,5,7,9
srinivas aytha
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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