Question

The sums of three numbers in A.P. is -3 and the product is 35. Find the numbers.

Answer 1

Hi ,

Let ( a - d ) , a , ( a + d ) are three numbers

in A. P

according to the problem given ,

Sum of the numbers = -3

a - d + a + a + d = -3

3a = -3

a = -3/3

a = -1 ----( 1 )

product of the numbers = 35

( a - d ) a ( a + d ) = 35

( a² - d² ) a = 35

[ ( -1 )² - d² ] ( -1 ) = 35

( 1 - d² ) = - 35

- d² = - 35 - 1

- d² = -36

d² = 36

d = ± √36

d = ± 6 -----( 2 )

Therefore ,

Required numbers are ,

i ) if a = -1 , d = 6

a - d = -1 - 6 = -7 ,

a = -1 ,

a + d = -1 + 7 = 6

Or

ii ) if a = -1 , d = -6

a - d = -1 - ( -6 ) = -1 + 6 = 5

a = -1

a + d = - 1 + ( - 6 ) = - 1 - 6 = -7

I hope this helps you.

: )

Answer 2

let take that A.P as
(a-d) , a , (a+d)

1)
(a-d) + a + (a+d) = -3

a -d + a + a + d = -3

3a = -3

a = -3/3

a = -1

2)

(a-d)(a)(a+d) = 35

(a²-d²)(a) = 35

a³ - ad² = 35

(-1)³ - (-1)(d²) = 35

-1 + 1d² = 35

d² = 35+1

d² = 36

d = √36

d = 6


so , the numbers are

a-d = -1-6 = -7

a = -1

a+d = -1+6 = 5

-7 , -1 , 5