x2+1/x2 এর নিম্নোক্ত কোন মানের জন্য x3 - 1/x3 = 0 হবে?
Solution
Correct Answer: Option D
x3 - 1/x3 = 0
=> (x-1/x) (x2 + x.1/x + 1/x2)= 0
=> (x - 1/x ) (x2 + 1/x2 + 1 ) =0
∴ x - 1/x =0 [ ∴ x2 + 1/x2 + 1 ≠ 0 ]
বা, ( x - 1/x )2 = 0 [ উভয়পক্ষে বর্গ করে ]
বা, x2 - 2.x.1/x + 1/x2 =0
∴ x2 + 1/x2 = 2
=> (x-1/x) (x2 + x.1/x + 1/x2)= 0
=> (x - 1/x ) (x2 + 1/x2 + 1 ) =0
∴ x - 1/x =0 [ ∴ x2 + 1/x2 + 1 ≠ 0 ]
বা, ( x - 1/x )2 = 0 [ উভয়পক্ষে বর্গ করে ]
বা, x2 - 2.x.1/x + 1/x2 =0
∴ x2 + 1/x2 = 2
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