Question

Find three numbers in Ap whose sum is 9 and product is -165

Answer 1

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Answer 2

Answer:

The three numbers are -5,3 and 11.

Step-by-step explanation:

Given : Three numbers in A.P whose sum is 9 and product is -165.

To find : The three number ?

Solution :

Let (a-d),a,(a+d) are three numbers in A.P.

The sum of three numbers is 9.

So, $a-d+a+a+d=9$

$3a=9$

$a=3$

The product of three numbers is -165.

So, $(a-d)a(a+d)=-165$

$(a^2-d^2)a=-165$

Substitute a=3,

$(3^2-d^2)3=-165$

$(9-d^2)=-\frac{165}{3}$

$d^2=9+55$

$d^2=64$

$d=\pm 8$

When a=3 and d=8,

a-d=3-8=-5

a=3

a+d=3+8=11

An A.P is -5,3,11.

When a=3 and d=-8,

a-d=3+8=11

a=3

a+d=3-8=-5

An A.P is 11,3,-5.

Therefore, The three numbers are -5,3 and 11.