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If a, b, c are three consicutive integers. Prove that, (a-i) (a+i) (c-i) (c+i) = b^4 + 1

If a, b, c are three consicutive integers. Prove that, (a-i) (a+i) (c-i) (c+i) = b^4 + 1

Grade:11

1 Answers

Vikas TU
14149 Points
3 years ago
Dear student 
 (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
So, in the question the RHS must be  b⁴ + 4
Good Luck 

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