Question

Sum of three numbers in AP is 15 and sum of their squars is 93 find the numbers

Answer 1

Similar problem like your query,i hope it will help you. Q;An ap consists of 3 terms whose sum is 15 and sum of the squares of the extremes is 58. Find the terms Let a-d, a ,a+d are three terms in AP
sum of three terms = 15
a-d+a+a+d =15
⇒3a=15
a=15/3
a= 5--(1)
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sum of the squares of the extremes = 58
(a-d)²+(a+d)²= 58
⇒2(a²+d²) =58
⇒a²+d²=58/2
⇒5²+d²= 29 [ from (1)]
⇒d² = 29-25
∴d²=4
d= 2 or -2
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required three terms are
if a=5 , d= 2
a-d, a, a+d
(5-2),5,(5+2)
3,5,7
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if a=5 , d=-2
[5-(-2)], 5, [5+(-2)]
7,5,3