Question

)The sum of four terms in an AP is 4 and product is 385.Find the numbers?

Answer 1

Answer:

11/3, -5/3, 9, -7

Step-by-step explanation:

Let the 4 numbers in A.P be

a-3d, a-d, a+d, a+3d

the sum of thse numbers is 4

a+d+a-d+a+3d+a-3d =4

4a=4

a=1

And the product is 385

(a-3d)(a+3d)(a+d)(a-d)=385

put a=1

(1-3d)(1+3d)(1+d)(1-d)=385

(1-9d²)(1-d²)=385

(1-d²-9d²+9d⁴)=385

9d⁴-10d²-384=0

d²=t

9t²-10t-384=0

9t²-64t+54t-384=0

t(9t-64)+6(9t-64)=0

(t+6)(9t-64)=0

t=-6, 64/9

d²=t

d=8/3

hence the numbers are

a=1, d=8/3

(a+d), (a-d), (a+3d), (a-3d)

11/3 , -5/3 , 9, -7

hope this will hlp u