Question : What is the HCF of (x6 + 1) and (x4 - 1)?
Option 1: 1
Option 2: (1 + x)
Option 3: (1 - x2)
Option 4: (1 + x2)
Answer (1)
9th Jan, 2024
Correct Answer: (1 + x 2 )
Solution :
Use :
$(a^{3} + b^{3}) = (a + b)(a^{2}− ab + b^{2})$
$a^{2} + b^{2} = (a + b)(a − b)$
So, $x^{6} + 1 = (x^{2})^{3} + 1^{3}$
= $(x^{2} + 1)(x^{4} − x^{2} + 1)$
Now,
$x^{4} − 1 = (x^{2} + 1)(x^{2} − 1)$
So,
HCF $(x^{6} + 1, x^{4} − 1) = (x^{2} + 1)$
Hence, the correct answer is $x^{2} + 1$
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