Question

the sum of 3 numbers of AP is 3. the product of 1st and 3rd number is -35. find the 3 numbers

Answer 1

this is the appropriate answer

Answer 2

$\huge\mathfrak\red{Answer :}$


Let the three number be... (a - d), (a) and (a + d)

And their sum is 3

So,

A.T.Q

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

a - d + a + a + d = 3

3a = 3

a = 1

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

(1 - d) (1 + d) = 1 - 35

1 (1 + d) [-d (1 + d)] = - 35

1 + d - d - d² = - 35

- d² = - 35 - 1

- d² = - 36

d² = 36

d = √36

d = ± 6

d = + 6 or - 6

If a = 1 and d = + 6

Then,

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

a = 1

a + d = 1 + 6 = 7

A.P. = -5, 1, 7

If we take a = 1 and d = -6

Then,

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

a = 1

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

A.P. = 7, 1, -5

The number we got are...

$\textbf{-5, 1, 7 or 7, 1, -5}$

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