in an ap the sum of first three terms is 15 and the sum of the square of extremes is 58 find the terms
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Let the there terms be a+d, a, a-d
sum of 3 terms=15
a+(a+d)+(a-b)=15
3a=15
a=5 ⇒1
sum of square of extremes=58
that is, (a+d)²+(a-d)²=58
d²+a²+2ad+d²+a²-2axd=58
2(a²+d²)=58
a²+d²=29
wkt, a=5 from equation 1
d²+5²=29
d²=29-25
d²=4
d= +2 or -2
if d=+2 then the terms are
5-2, 5, 5+2= 3, 5, 7
if d=-2 then terms are
5-(-2), 5, 5+(-2)= 7, 5, 3
sum of 3 terms=15
a+(a+d)+(a-b)=15
3a=15
a=5 ⇒1
sum of square of extremes=58
that is, (a+d)²+(a-d)²=58
d²+a²+2ad+d²+a²-2axd=58
2(a²+d²)=58
a²+d²=29
wkt, a=5 from equation 1
d²+5²=29
d²=29-25
d²=4
d= +2 or -2
if d=+2 then the terms are
5-2, 5, 5+2= 3, 5, 7
if d=-2 then terms are
5-(-2), 5, 5+(-2)= 7, 5, 3
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