x2 = 3x - 1 হলে (x8 + 1)/x4 এর মান কত?
Solution
Correct Answer: Option A
দেওয়া আছে,
x2 = 3x - 1
বা, x2 + 1 = 3x
বা, x2/x + 1/x = 3x/x
বা, x + 1/x = 3
(x8 + 1)/x4 = x8/x4 + 1/x4
= x4 + 1/x4
= (x2)2 + (1/x2)2
= (x2 + 1/x2)2 - 2.x2.1/x2
= {(x + 1/x)2 - 2.x.1/x}2 - 2
= {32- 2}2 - 2
= (9 - 2)2 - 2
= 72 - 2
= 49 - 2
= 47
x2 = 3x - 1
বা, x2 + 1 = 3x
বা, x2/x + 1/x = 3x/x
বা, x + 1/x = 3
(x8 + 1)/x4 = x8/x4 + 1/x4
= x4 + 1/x4
= (x2)2 + (1/x2)2
= (x2 + 1/x2)2 - 2.x2.1/x2
= {(x + 1/x)2 - 2.x.1/x}2 - 2
= {32- 2}2 - 2
= (9 - 2)2 - 2
= 72 - 2
= 49 - 2
= 47
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