ল.সা.গু নির্ণয় করুন। a3- 1, 1 + a3, 1 + a2 + a4
Solution
Correct Answer: Option A
১ম রাশি = a3 - 1
= a3 - 13
= (a - 1)(a2 + a + 1)
২য় রাশি = 1 + a3
= a3 + 13
= (a + 1)(a2 - a + 1)
৩য় রাশি = 1 + a2 + a4
= a4 + 2a2 + 12 - a2
= (a2 + 1)2 - a2
= (a2 + 1 + a)(a2 + 1 - a)
= (a2 + a + 1)(a2 - a + 1)
নির্ণেয় ল.সা.গু = (a - 1)(a2 + a + 1)(a + 1)(a2 - a + 1)
= (a3 - 1)(a3 + 1)
= (a3)2 - 12
= a6 - 1
= a3 - 13
= (a - 1)(a2 + a + 1)
২য় রাশি = 1 + a3
= a3 + 13
= (a + 1)(a2 - a + 1)
৩য় রাশি = 1 + a2 + a4
= a4 + 2a2 + 12 - a2
= (a2 + 1)2 - a2
= (a2 + 1 + a)(a2 + 1 - a)
= (a2 + a + 1)(a2 - a + 1)
নির্ণেয় ল.সা.গু = (a - 1)(a2 + a + 1)(a + 1)(a2 - a + 1)
= (a3 - 1)(a3 + 1)
= (a3)2 - 12
= a6 - 1
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