x3 - 1, x3 + 1, x4 + x2 + 1 এর ল. সা. গু. কত?
Solution
Correct Answer: Option C
১ম রাশি = x3 - 1
= x3 - 13
= (x - 1)(x2 + x + 1)
২য় রাশি = x3 + 1
= x3 + 13
= (x + 1)(x2 - x + 1)
৩য় রাশি = x4 + x2 + 1
= (x2)2 + 2.x2 .x + 12 - x2
= (x2 + 1)2 - x2
= (x2 + 1 + x)(x2 + 1 - x)
= (x2 + x + 1)(x2 - x + 1)
নির্ণেয় লসাগু = (x - 1)(x2 + x + 1)(x + 1)(x2 - x + 1)
= (x3 - 13)(x3 + 13)
= (x3 - 1)(x3 + 1)
=(x3)2 - 12
= x6 - 1
= x3 - 13
= (x - 1)(x2 + x + 1)
২য় রাশি = x3 + 1
= x3 + 13
= (x + 1)(x2 - x + 1)
৩য় রাশি = x4 + x2 + 1
= (x2)2 + 2.x2 .x + 12 - x2
= (x2 + 1)2 - x2
= (x2 + 1 + x)(x2 + 1 - x)
= (x2 + x + 1)(x2 - x + 1)
নির্ণেয় লসাগু = (x - 1)(x2 + x + 1)(x + 1)(x2 - x + 1)
= (x3 - 13)(x3 + 13)
= (x3 - 1)(x3 + 1)
=(x3)2 - 12
= x6 - 1
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