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