Question

If a, b, c are 3 consecutive integers prove that 4 (a-i )(a+i )(c+i )( c-i) =b^4 +1

Answer 1

(a-i )(a+i )(c+i )( c-i) =b⁴ + 4

Step-by-step explanation:

a, b, c are 3 consecutive integers

a = b - 1

c = b + 1

 (a-i )(a+i )(c+i )( c-i) =b⁴ + 4

LHS =

 (a-i )(a+i )(c+i )( c-i)

= (a² - i²)(c² - i²)

i² = - 1

= (a² + 1)(c² + 1)

= a² + c²  + a²c²  + 1

= (b - 1)² + (b + 1)²  + (b-1)²(b + 1)² + 1

= b² + 1 - 2b + b² + 1 + 2b  + (b² - 1)² + 1

= 2b² + 3  + b⁴ + 1 - 2b²

= b⁴ + 4

= RHS

QED

Proved

Learn more:

1 + iota ki power 4 upon 1 minus iota cube whole power 4

https://brainly.in/question/10010687

activity to interpret the meaning of iota and its integral power ...

https://brainly.in/question/12311848