11. Find four numbers in AP whose sum is 28 and the sum of whose squares
is 216.
Answers
Answered by
2
ANSWER
Let the numbers be, a−3d,a−d,a+3d,a+d
Given,
a−3d+a−d+a+3d+a+d=28⇒4a=28,∴a=7
(a−3d)
2
+(a−d)
2
+(a+3d)
2
+(a+d)
2
=216
2(a
2
+9d
2
)+2(a
2
+d
2
)=216
4a
2
+20d
2
=216
4(7
2
)+20d
2
=216⇒d=±1
for d=1
the series is 7−3(−1),7−(−1),7−1,7−3⇒10,8,6,4
For d=1
the series is 7−3,7−1,7+1,7+3⇒4,6,8,10
Therefore the numbers are, 4,6,8,10
Similar questions