Question

if a, b, c and d are consecutive odd numbers, then ( a^2 + b^2 + c^2 + d^2 ) is always divisible by
(a) 4
(b) 5
(c) 7
(d) 8

Answer 1

Answer:

(a)

Step-by-step explanation:

by taking 1,3,5,7 in the place of a,b,c,d by squaring they are divided by exactly by 4

Answer 2

Therefore the value ( a² + b² + c² + d² ) is always divisible by '4'. ( Option-a )

Given:

a, b, c and d are consecutive odd numbers.

To Find:

The value ( a² + b² + c² + d² ) is always divisible.

Solution:

The given question can be solved as shown below.

Let a = 1, b = 3, c = 5, and d = 7

Then a² = 1, b² = 9, c² = 25, and d² = 49

Then, a² + b² + c² + d² = 1 + 9 + 25 + 49 = 84

As the sum of 4 odd numbers is always even so it is not divisible by '5' and '7'.

And 84 is not divisible by '8'.

So finally 84 is not divisible by '4'.

Therefore the value ( a² + b² + c² + d² ) is always divisible by '4'.

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