CBSE BOARD X, asked by infantanto180575, 1 year ago

the sum of the first three number in an ap is 18 if the product of first and third team is 5 times the common difference find the three no.s


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Answers

Answered by Anonymous
4


Hey mate ☺
Latest question asked in CBSE Maths examination 2019

SoLuTiOn :

let a1= g-d

a2= g

a3=g+d

A.T.Q

g-d+g+g+d=18

3g=18

g=6

(g-d)(g+d)=5d

 {g}^{2} - d^{2} = 5d

put g=6

36 - {d}^{2} = 5d

d ^{2} + 5d - 36 = 0

a=1

b=5

c=-36

discriminat =

b ^{2} - 4ac

 {5}^{2} - 4(1)( - 36) \\ d = 25 + 144 \\ d = 169 \\ \sqrt{d} = 13

d = \frac{ - b + \sqrt{d} }{2a} or \frac{ - b - \sqrt{d} }{2a} \\ = \frac{ - 5 + 13}{2} or \frac{ - 5 - 13}{2} \\ = \frac{8}{2} \: or \frac{ - 18}{2} \\ = 4 \: or - 9

when d=4

terms are :

6-4=2

6

6+4=10

AP: 2,6,10...and so on

when d=-9

6-(-9)=15

6

6-9=-3

AP:15,6,-3...and so on

Hope it helps you ☺✌✌
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