Question

In an ap sum of 3 numbers is 45 and their product is 3135. find out the numbers

Answer 1

sum of 3 no. 'S = 45
(a) + (a + d) + (a + 2d) = 45
3a + 3d = 45
3(a + d) = 45
(a + d) = 45/3
a + d = 15
d = 15 - a
It means the 3 no. 's is a ,
[(a + d)] = [a + (15 - a)] = {15} ,
[(a + 2d)] = [a + 2(15 - a)] = [a + 30 - 2a] = {30 - a}

the three no. 's is a , 15 , (30 - a)

product of three no. 's is 3135
a * 15 * (30-a) = 3135
15a * (30-a) = 3135
a * (30-a) = 3135/15
a * (30-a) = 209
$30a - {a}^{2} = 209$
${a}^{2} - 30a - 209 = 0$
${a}^{2} - 11a - 19a - 209 = 0$
a(a - 11) - 19(a - 11) = 0
(a-11)(a-19)=0
a = 11 or 19


If a = 11 then d = 4
so the three no. 's is 11 , 15 , 19


If a = 19 then d = -4
so the three no. 's is 19 , 15 , 11


Hence, the no.s is 11 , 15 , and 19.