x4 - x2 + 1 = 0, হলে x3 + 1/x3 = কত?
Solution
Correct Answer: Option D
x4 - x2 + 1 = 0
বা, x4 + 1 = x2
বা, x4/x2 + 1/x2 = x2/x2
বা, x2 + 1/x2 = 1
বা, (x + 1/x)2 - 2.x.1/x = 1
বা, (x + 1/x)2 - 2 = 1
বা, (x + 1/x)2 = 1 + 2
বা, (x + 1/x)2 = 3
(x + 1/x) = √3
x3 + 1/x3 =(x + 1/x)3 - 3.x.1/x(x + 1/x)
= (√3)3 - 3√3
= 3√3 - 3√3
= 0
বা, x4 + 1 = x2
বা, x4/x2 + 1/x2 = x2/x2
বা, x2 + 1/x2 = 1
বা, (x + 1/x)2 - 2.x.1/x = 1
বা, (x + 1/x)2 - 2 = 1
বা, (x + 1/x)2 = 1 + 2
বা, (x + 1/x)2 = 3
(x + 1/x) = √3
x3 + 1/x3 =(x + 1/x)3 - 3.x.1/x(x + 1/x)
= (√3)3 - 3√3
= 3√3 - 3√3
= 0
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