Question

find 4numberes in ap whose sum is10 and sum of squares is 30​

Answer 1

Answer:

Step-by-step explanation:

let the 4 terms of the AP be, (a - 3d), (a - d), (a + d) and (a + 3d)  having 2d as the common difference.

given,

a-3d + a-d + a+d + a+3d = 10

=> 4a = 10

=> 2a = 5

=> a = 5/2 ----------------- (1)

also, (a-3d)²+(a-d)²+(a+d)²+(a+3d)² = 30

=> (a²-2(a)(3d)+(3d)²) +  (a²-2ad+d²) + (a²+2ad+d²) + (a²+2(a)(3d)+(3d)²) = 30

=> a²-6ad+9d²  +  2(a²+d²) +  a²+6ad+9d²

=>  2(a²+9d²) + 2(a²+d²) = 15

=> 2(a²+a²+9d²+d²) = 15

=> 2(2a²+10d²) = 15

=> 4(a²+5d²) =15

=> a²+5d² = 15/4

substituting a=5/2 in the above eqn.

we get,

(5/2)² + 5d² = 15/4

(25/4) + 5d² = 15/4

5d² = 15/4 - 25/4

5d² = 5(3/4 - 5/4)

d² = (3-5)/4

d² = -2/4 = -1/2

d = 1/√2