Question

the sum of three no of an AP is 3 and product of first and the third no is -35. Find the three no​

Answer 1

Step-by-step explanation:

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the sum of three numbers in an arithmetic progression is 15 and their product is 105. Find the numbers It has to do with Arithmetic Progression and the formula

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Expert Answers info

RICO GRANT eNotes educator | CERTIFIED EDUCATOR

Let x,x+d and x+2d be the three numbers.

Then x+x+d+x+2d=15 or 3x+3d=15 ==>x+d=5

We are also given x(x+d)(x+2d)=105

Substituting 5-x for d we get:

x(x+5-x)(x+2(5-x))=105

x(5)(-x+5)=105

-5x^2+50x=105

5x^2-50x+105=0

5(x-3)(x-7)=0 so x=3 or x=7

If x=7 then d=-2 and we have 7,5,3 as the numbers.

If x=3 then we have 3,5,7 as the numbers.

Answer 2

let the 3 numbers of an AP is

a-d,a,a+d

according to question the sum of three number is 3

so

a-d+a+a+d=3

3a=3

a=1

now according to question

(a-d)×(a+d)=-35

so a^2-d^2=-35

now as we got a=1

so d^2 = 36

so d=6

so numbers are

-5,6,7